2023 – a Year of Magnitude and Direction

2023 marked year 15 for Endurica.  If I had to pick one word to describe the past year, that word would be “vector”.  Because magnitude and direction.  😊

We updated our core value statement this year.  The first one I ever wrote as part of Endurica’s original business plan listed 3 values: technical leadership, customer focus, and trustworthiness.  Those values served us well for many years and in many ways shaped who we have become.  But it was important this year to take stock again.  We’ve grown 8-fold since I wrote those down!  So our team spent many hours revisiting our shared values and deliberating over which will best define our culture and steer us right going forward.  In the end, we decided to keep the first 3, and we added 3 more:  embrace the grit, make an impact, and better every day.

We also completed an exercise to articulate what makes Endurica truly unique in the CAE / durability simulation space.  The 3 words we chose are… Accurate, Complete, and Scalable.

  • Accurate refers to the accurate material models that capture rubber’s many “special effects”, the accurate critical plane analysis method for analyzing multiaxial history, the accurate handling of nonlinear relationships between global input load channels and local crack experiences, and the extensive set of validation cases that have demonstrated our accuracy over the years. Nobody offers a more accurate solution for rubber durability.
  • Complete refers to our complete coverage of infinite life, safe life and damage tolerant approaches to testing and simulation. It refers to feature completeness that enables users to account for nearly any material behavior under nearly any service conditions.  Finally, it refers to the documentation, the materials database, and the examples we distribute with the software and with our webinar series.  Nobody offers a more complete solution for rubber durability.
  • Scalable refers to our capacity to apply our solutions efficiently in all circumstances. Scalability is the training we provide so that users can learn our tools quickly.  Scalability is access to powerful, ready-to-use workflows right when you need them.  Scalability is the modular approach we take to material testing and modeling so that simple problems can be solved cheaply and complex problems can be solved accurately in the same framework.  Scalability is our multi-threading that allows job execution time to be accelerated to complete impactful analysis on tough deadlines.  Nobody offers a more scalable solution for rubber durability.

2023 was not all navel-gazing and new marketing.  We also had magnitude and direction in other areas.

Top 10 Code Developments:

  1. New Endurica Architecture: After several years of development and a soft launch under the Katana project name, we finally completed our migration to the new architecture.  The new architecture provides a huge speed advantage for single thread and now for multithread execution. It uses a new input file format (.json). The json format makes it easier than ever for users to build customized and automated workflows via Python scripting.
  2. Sequence Effects: Sometimes the order of events matters to durability, and sometimes it doesn’t. We introduced Steps and Blocks to our input file, giving users complete control over the specification of multi-block, multi-step scheduling of load cases.  There is also a new output request that came out of this work: residual strength.
  3. EIE: 6 channels and support for RPC: Support for 6 channels of load input was one of our most highly requested new features.  Fast growing use of this feature led to further enhancements of the workflow (support for rpc file format, studies of map building techniques), and new recommendations on how to implement boundary conditions for specified rotation histories in explicit and implicit finite element models.
  4. Queuing: Design optimization studies need efficient management and execution of multiple jobs. Endurica’s software license manager now supports queueing for licenses. Queuing allows a submitted job to automatically wait to start until a license is available, instead of the prior behavior of exiting with a license error. Now you can submit many jobs without worrying about license availability.
  5. Haigh Diagram Improvements: We implemented an improved discretization of the Haigh diagram, and parallelized its evaluation. Now you get much nicer looking results in a fraction of the time. For details, check out our blog post on Haigh diagrams and also read about other improvements like axis limit setting and smoother contour plots.
  6. Viewer image copy: There is now a button! Its easier than ever to get your images into reports.
  7. Documentation Updates: We have been focusing on improving documentation this year. There are many new sections in the theory manual and user guide, as well as a getting started guide and more examples.  Stay tuned for many more examples coming in 2024!
  8. User Defined Planes: It is now possible to define your own set of planes for the critical plane search. One example where you might want to do this would be the situation where you would like to refine the critical plane search on a limited domain of the life sphere.
  9. New Database Materials: We added 7 new carbon black and silica filled EPDM compounds to the database. We are now up to 42 unique rubber compounds in the database.
  10. Uhyper Support: The new architecture now supports user-defined hyperelasticity. If you have a Uhyper subroutine for your finite element analysis, you can use it directly with Endurica.

 

Testing Hardware

We completed the acquisition and installation at ACE labs of a Coesfeld Instrumented Cut and Chip Analyser (ICCA).  The ICCA provides unmatched measurement and control of impact conditions, and provides a way to evaluate rubber compounds for their resistance to cutting and chipping.

 

Applications, Case Studies, Webinars

Never underestimate the students! We were blown away by the work of undergraduates at the University of Calgary with our tools and Ansys.  The students designed an airless tire, completing durability simulations using Endurica software within the scope of a senior design project. They were able to Get Durability Right on a short timeline and a student budget. Check out their multi-objective, high-performance design project here.

Analyzing what happens to tires as they take on the most celebrated testing track in the world might have been the funnest project Endurica’s engineers tackled in 2023. We presented the technical details at The Tire Society annual meeting and more in a followup webinar. An extensive Q&A session followed, and I loved the final question: “So, how long before we have a dashboard display of ‘miles to tire failure’ in our cars?”  Bring it.  We are ready!

Our Winning on Durability webinar series hit a nerve with the Metal Fatigue DOES NOT EQUAL Rubber Fatigue episodes on mean strain (the tendency of larger mean strains to significantly INCREASE the fatigue life of some rubbers!) and linear superposition (for converting applied load inputs to corresponding stress/strain responses). The great response has lead to our third installment on the differences between rubber and metal fatigue with an upcoming presentation on temperature effects.

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The 5-50-500 Rule

The 5, 50, 500 Rule with dice showing Chance to Change

2 Minute Read | 400 Words

I ran a marketing consulting business for 30 years before joining Endurica and tried to save clients from learning the hard way. When brochures were the only way to convey a company’s message (pre-internet), it was critical that people understood the $5, $50, $500 rule.

  • $5 = cost for changes during the earliest design phase. This is the point where everything is on the table as you develop the look, feel, message, and content of the brochure.
  • $50 = cost to make changes at the first mock-up of the brochure. No big deal. At this stage, changes take a bit of work and may impact multiple pages or sections – but it’s a LOT better to make changes now than later and I encouraged people to speak up about anything/everything because change was still pretty easy. Approval at this stage sends us into production.
  • $500 = cost to make changes after we sent the brochure to the printer. That’s the cost to change even one LETTER, let alone a photo or – heaven forbid – an entire page. It was at this point that one client said “ok, now I’ll read it” and I had to stop myself from throwing a file at him.

All of this came up as we talked about the value of our software in rubber product development. The concept’s the same but the numbers are SO MUCH BIGGER. “Add about 3 zeroes to each of those steps,” remarked Tom Ebbott, Endurica’s VP and newest team member. “It’s the same concept in tire development but the impact is just so much bigger.

From a technical side, one of our client’s says it best: “In optimizing a geometry to extend the fatigue life of a product I ran a few iterations of inner-cavity geometries, and found one specific geometry with Endurica that achieved 500,000 cycles to failure in contrast to the 30,000 I had before. It’s more than a 10-time improvement and that’s really significant. These concrete numbers are really powerful in helping us and our customers to make good decisions.” Francois Rouillard, R&D Mechanical Engineer, Maestral Sealing Laboratory, Technetics, Pierrelatte, France.

WHY IT MATTERS: Endurica’s users find THE BEST solution to their client’s problem early — at the $5,000 stage of design. They can skip the multiple iterations that easily run $50,000 each and go right into the $500,000 production testing cycle with complete trust in the product’s success.

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Busting Myths About Endurica

Myths vs Facts on Endurica, Test your knowledge about Endurica

True or False? Test your knowledge about Endurica

Endurica is only a software company.
False. While Endurica is perhaps best known for its game-changing fatigue solver software, we also deliver industry-leading testing services, testing instruments, and training.  If you need durability for elastomers, we are uniquely positioned to bring you winning capabilities.

Endurica is used by the majority of top rubber product makers.
True.  As of the 2021 Rubber News global rankings report, 6 of the top 9 global rubber product makers are using Endurica solutions to characterize and simulate durability.

Endurica invented Critical Plane Analysis.
False, but...  Critical Plane Analysis – the technology that gives best accuracy fatigue life predictions under complex multiaxial loading – was originally pioneered by the metals fatigue community.  But Endurica does hold the patent on the first Critical Plane Analysis algorithm suitable for elastomers, and we are the world leaders in making the technology available to product developers.

Wohler curve based methods are just as accurate and competitive as Endurica’s Critical Plane / Fracture Mechanics-based method.
False. Wohler curve based methods suffer from many problems that are solved by the Critical Plane Method.  1) they often assume a wrong crack orientation rather than searching for the most damaging scenario, 2) they do not account properly for mode of deformation effects, 3) the testing program required to populate a Wohler curve scales poorly and has poor repeatability.

I don’t need Endurica software if I already have a metal fatigue code (nCode DesignLife, FEMFAT, MSC Fatigue, and fe-safe).
False. Metals and elastomers have completely distinct molecular structures and behaviors.  While metals operate at small strain, elastomers tend to operate at large strain.  Where metals exhibit linear elasticity, elastomers exhibit nonlinear behavior.  Using a metal fatigue code for analyzing elastomer fatigue is like trying to use a car as a boat: you can certainly drive the car into the water, but you end up on the bottom of the lake.

Endurica solvers work with Ansys, Simulia, and Hexagon simulation platforms
True. We maintain software development partnerships with the major finite element software vendors so that we can offer easy to use pre-and post- integrations with Ansys, Abaqus, and MSC/Marc.  You can use the Endurica workflows with the finite element code that works for you.  We also develop the fe-safe/Rubber plugin.

Everyone knows you can simulate durability.
False. We’re always surprised by the number of people at conferences and trade shows who don’t know that simulating the durability of rubber is even possible.  Our tools simulate everything from basic constant amplitude cyclic loading, to variable amplitude, multiaxial loading (up to 6 input channels!), ageing, strain crystallization, ozone attack, cyclic softening, creep crack growth, self-heating, block cycle schedules, residual life.  Our multi-threading capabilities mean that large jobs can execute quickly.  Our solvers are fast enough to compute damage in real-time for a full finite element model!

Endurica solutions have had significant commercial impact.
True.  Endurica was founded in 2008 to reduce rubber product launch cost and risk and we have saved our clients millions of dollars.  Endurica’s impact was recognized with the prestigious U.S. Small Business Administration Tibbetts award.

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Virtual vs. Physical in 2021 and Beyond

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.

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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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So This Happened on the Show Floor at IEC2019

Convention Floor

“I tell my suppliers to use you all the time.”  – Exact words from an engineer in charge of purchasing key components for a major automaker when he stopped by our booth at the International Elastomers Conference in Cleveland.

“Not all of them listen and there’s one I really wish would hear me. They tell me ‘there is no money for more software and testing’. But we use your software internally and we KNOW it can help them. This supplier has been working on a bushing for us for over a year and they still can’t hit our requirements.”

He went on to tell me how the supplier’s current design is not sufficiently evolved. How it is too risky. How it might compromise vehicle performance.  How he can’t take chances.  How he sure wished they would hear what he’s been saying because he really doesn’t want to pull their business and go to another source but he is running out of time. “I can’t wait much longer.”

“We could use your tools, but profits are measured in pennies. Rubber is a tough industry with low margins and high competition.”  – Exact words spoken probably 15 minutes later from an engineer with a major Tier 2 supplier. This fellow went on to lament how he just had equipment moved out of his facility to another division after losing a contract with a big customer.  “Corporate” decided the equipment would be better utilized elsewhere.  “It’s hard for us to bring in new technology unless our customers will pay for it.”

“Look at the ROI.” – Exact words from Endurica’s president as we were discussing these conversations after the show.  We give out 100 Grand bars at our booth to kick start this kind of conversation, but there is easily more than $100,000/year at stake.  Have you ever calculated your development costs? What if you had durability right the first time, every time? Here is a typical scenario – you can put in your own numbers.  This isn’t the only way to estimate the ROI.  You could also come at it like we did here, or here.

Traditional Development Process With Endurica
Compound Selection 2 months + $20,000 Same
Product Design 2 months + $20,000 3 months + $30,000
Mold and Tooling 6 months + $50,000 Same
Prototype Production 3 months + $25,000 Same
Component Testing 3 months + $25,000 Same
Fleet/Field Testing 12 months + $100,000 Same
Regulatory Compliance 1 month + $10,000 Same
Sub-total, Per Iteration Cost 12 months + $250,000 12 months + $260,000
Development iterations per project launch 2x Right the first time
Total Cost 24 months + $500,000 12 months + $260,000
Savings with Endurica,
per product launch
12 months + $240,000

 Cost of Qualifying Fatigue Performance | 100 Grand

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Behind the Scenes Tour of Endurica Software Development and QA Practices

Ever wonder what it takes to consistently deliver quality and reliability in our software releases?  Here’s a brief overview of the systems and disciplines we use to ensure that our users receive timely, trouble-free updates of Endurica software.

Automation:

Throughout the life of our software, changes are made to our source code for a variety of reasons.  Most commonly, we are adding new features and capabilities to our software.  We also make updates to the code to improve performance and to squash the inevitable bugs that occasionally occur.

With each change committed to the code repository, the software needs to be built, tested, and released.  Endurica’s workflow automates these steps so that any change to the source repository triggers a clean build of the software.  A successful build is automatically followed by a testing phase where our suite of benchmarks is executed and compared to known results.  Finally, the build is automatically packaged and stored so that it is ready to be delivered.  At each step along the way, a build error or failed test will cancel the workflow and send an alert warning that the release has been rejected, so that the issue can be addressed, and the workflow restarted.

Endurica's build and testing process ensures that high quality standards are met for every new release. Black arrow: normal flow, Red arrow: an error or failed test
Figure 1: Endurica’s build and testing process ensures that high quality standards are met for every new release. Black arrow: normal flow, Red arrow: an error or failed test.

Reliability:

The automated testing phase that every release goes through helps ensure the reliability of our software.  For example, every Endurica CL release must pass all 70 benchmarks.  Each benchmark is a separate Endurica CL analysis made up of different materials, histories, and output requests.  Results from a new build are compared to known results from the previous successful build.  If results do not agree, or if there are any errors, the benchmark does not pass and the build is rejected.

The testing phase prevents “would-be” bugs from making it into a release and makes sure that any issues get resolved.

Repeatability:

The automated nature of our development workflow naturally helps with repeatability in our releases.  Each build flows through the same pipeline, creating consistent releases every time.  There is less worry, for example, that a component will be forgotten to be included.  It also allows us to recreate previous versions if comparisons need to be made.

Traceability:

Our version control system enables us to easily pinpoint where and when prior changes were introduced into the software.  Each release is tied to a commit in the repository. This allows any future issues to be easily traced back and isolated to a small set of changes in the source for quick resolution.

Responsiveness:

Automating the build and release pipelines greatly increases our responsiveness.  If an issue is discovered in a release, the problem can be resolved, and a fully corrected and tested release can be made available the same day.  We can also quickly respond to user feedback and suggestions by making small and frequent updates.

The systems and disciplines we use in our development process make us very efficient, and they protect against many errors. This means we can spend more of our time on what matters: delivering and improving software that meets high standards and helps you to get durability right.

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Will Mars on the Rubber Industry: A Look Back 10 Years, Where We Are Now, A Look Ahead 10 Years

 Dr. William V. Mars Q: With regards to fatigue life prediction methods, where was the rubber industry 10 years ago?

Will There was plenty of great academic work and good understanding of fundamentals, but the methods were only deployed – if at all – via “homebuilt” solutions that could never support a broad enough audience to really impact daily product design decisions.  Simulation methods and experimental methods shared theoretical foundations but they were poorly integrated.  They suffered from operational problems, noisy data and open-ended test duration.  It was possible to analyze a crack if you could mesh it, but the added bookkeeping and convergence burdens were usually not sustainable in a production engineering context.  Mostly, analysts relied on tradition-based crack nucleation approaches that would look at quantities like strain or stress or strain energy density.  These were not very accurate and they were limiting in many ways, even though they were widely used.  They left companies very dependent on build and break iterations.

Q: Where is the industry today?

Will: The early adopters of our solutions have been off and running now for a number of years.  Our critical plane method has gained recognition for its high accuracy when dealing with multiaxial cases, cases involving crack closure, cases involving strain crystallization.  Our testing methods have gained recognition for high reliability and throughput.  Our users are doing production engineering with our tools.  They are consistently winning on durability issues.  They are handling durability issues right up front when they bid for new business.  They are expanding their in-house labs to increase testing capacity and they are winning innovation awards from OEMs.  They are using actual road-load cases from their customers to design light-weight, just-right parts that meet durability requirements.  The automotive industry has lead adoption but aerospace, tires, energy, and consumer products are also coming up.  We have users across the entire supply chain: raw material suppliers, component producers and OEMs.  The huge value that was locked up because durability was previously so difficult to manage is now unlocked in new ways for the first time.  This has been the wind in Endurica’s sails for the last 10 years.

Q: Where do you see the industry in 10 years?

Will: In 10 years, OEMs will expect durability from all component producers on day 1, even for radical projects.  They will expect designs already optimized for cost and weight.  They will push more warrantee responsibility to the supplier.  They will monitor durability requirements via shared testing and simulation workflows.  Suppliers will pitch solutions using characterization and simulation to show their product working well in your product.  The design and selection of rubber compounds to match applications will enter a golden age as real-world customer usage conditions will finally be taken fully into account.  Where design and selection was previously limited by the budget for a few build and break iterations, and low visibility of design options, they will soon be informed by an almost unlimited evaluation of all possibilities.  Where simulation methods have traditionally had greatest impact on product design functions, we will also start to see rubber part Digital Twins that track damage accumulation and create value in the operational functions of a business.  Durability is definitely set to become a strong arena for competition in the next 10 years.

 

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Durability Simulation and the Value of Product Development Resources

Durability Simulation | Endurica

What value does your company gain by deploying product development resources one way vs. another when it comes to durability?

R&D organizations are built around what it takes to get the product into production.  The costs of the organization include wages for the engineers and technicians, the costs of the capital equipment used in development and testing, and the overhead from administrative functions.  These are all fixed costs, and in the rubber industry it is typical to see R&D budgets that amount to somewhere between 1% and 5% of sales.

The R&D program lifecycle is iterative.  It goes something like this: design, build, test, qualify for production, launch product.  A quick way to understand product development costs is to look at how long it takes for one design-build-test-launch iteration.  If it takes your tech center one year per iteration, then the cost of one pass through the cycle is something like (company annual sales) x (R&D rate per annual sales)/(number of parallel development programs executing at a given time in your tech center).  For a $2B company with a 2.5% research budget and 10 development programs in the works, this works out to $5M/iteration.

An overview of cost distribution using the build and break method

How much of this cost is burned on durability issues?  Potentially all of it, at least within any one given iteration.  At worst, a non-qualifying test result leads to a “back to the drawing board” restart of the iteration.  The durability tests required for qualification can only be made after the prototype is in hand, so a restart means the whole team ends up revisiting and reproducing to correct a failed iteration.  Over the long run, if your iteration failure rate is 1 in 5 iterations (20%), that means you are burning $5M x 20% = $1M per product.

How much of this cost can realistically be avoided?  The big opportunity lies in the fact that the old “build and break” paradigm does not immediately hold accountable design decisions that lead to poor durability, and it does not have enough band-width to allow for much optimization.  A “build and break” only plan is a plan for business failure.  Poor decisions are only tested and caught after big investments in the iteration have all become sunk costs.  The advent of simulation has fueled a new “right the first time” movement that empowers the engineer to very rapidly investigate and understand how alternative materials, alternative geometries, or alternative duty cycles impact durability.  The number of alternatives that can be evaluated and optimized by an analyst before committing other resources is many times greater.  “Right the first time” via simulation is a model that is increasingly favored by OEMs and suppliers because it works.  Expect to halve your iteration failure rate.

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Tire Society 2017 – Best Question

Best Question Answer | 56.8 C - Peak temperature | N = 3.8E7 cycles = 131E3 km Cycles to 1 mm Crack

Every year, the top minds from academia, government and industry gather in Akron to share their work at the Tire Society annual meeting, and to enjoy a few moments of professional camaraderie.  Then we all return to fight for another year in the trenches of the technology wars of our employers.

This year, the meeting offered the latest on perennial themes: modal analysis, traction, materials science, noise, simulation, wear, experimental techniques for material characterization and for model validation.  Too much to summarize with any depth in a blog post.  If you are interested, you should definitely resolve to go next year.  Endurica presented two papers this year.

I presented a demonstration of how the Endurica CL fatigue solver can account for the effects of self-heating on durability in a rolling tire.  Endurica CL computes dissipation using a simple microsphere model that is compatible, in terms of discretization of the shared microsphere search/integration domain, with the critical plane search used for fatigue analysis.  In addition to defining dissipative properties of the rubber, the user defines the temperature sensitivity of the fatigue crack growth rate law when setting up the tire analysis.  In the case considered, a 57 degC temperature rise was estimated, which decreased the fatigue life of the belt edge by a factor of nearly two, relative to the life at 23 degC.  The failure mode was predicted at the belt edges.  For 100% rated load, straight ahead rolling, the tire was computed to have a life of 131000 km.

The best audience question was theoretical in nature: are the dissipation rates and fatigue lives computed by Endurica objective under a coordinate system change?  And how do we know?  The short answer is that the microsphere / critical plane algorithm, properly implemented, guarantees objectivity.  It is a simple matter to test: we can compute the dissipation and fatigue life for the same strain history reported in two different coordinate systems.  The dissipation rate and the fatigue life should not depend on which coordinate system is used to give the strain history.

For the record, I give here the full Endurica input (PCO.hfi) and output (PCO.hfo) files for our objectivity benchmark.  In this benchmark, histories 11 and 12 give the same simple tension loading history in two different coordinate systems.  Likewise, 21 and 22 give a planar tension history in two coordinate systems.  Finally, 31 and 32 give a biaxial tension history in two coordinate systems.  Note that all of the strain histories are defined in the **HISTORY section of the .hfi file.  In all cases, the strains are given as 6 components of the nominal strain tensor, in the order 11, 22, 33, 12, 23, 31.  The shear strains are given as engineering shear components, not tensor (2*tensor shear = engineering shear).

The objectivity test is successful in all cases because, as shown in the output file PCO.hfo, both the fatigue life, and the hysteresis, show the same values under a coordinate system change.  Quod Erat Demonstrondum.

ObjectivityTable

the full Endurica input (PCO.hfi) and output (PCO.hfo) files for the objectivity benchmark

 

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