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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My SAE WCX 2022 Top Takeaway

 

SAE WCX | Detroit, Michigan | April 5-7, 2022

There were several papers on fatigue life prediction for elastomers at SAE WCX 2022, but the highlight for us was this one from Automotive OEM Stellantis: “Fatigue Life Prediction and Correlation for Powertrain Torque Strut Mount Elastomeric Bushing Application” by Dr. Touhid Zarrin-Ghalami, Durability Technical Specialist at FCA US LLC Fiat Chrysler Automobiles logowith coauthors C Elango, Sathish Kumar Pandi, and Roshan N. Mahadule from FCA Engineering India Pvt, Ltd.  Check out the abstract or buy the paper here…

The study shows that very accurate fatigue life prediction results are possible for elastomeric components under block cycle loading using Critical Plane Analysis.  A key feature of the analysis is the characterization and modeling of rubber’s hyperelastic properties, fatigue crack growth properties, crack precursor size, and strain crystallization behavior.  Careful measurement of these analysis ingredients led to a nearly perfect correlation of the predicted life (520 blocks) with the tested life (523 blocks, average of 4 replicate tests), and of predicted failure mode with observed failure mode.

Endurica users like Stellantis are developing a solid track record of routine and successful fatigue life prediction.  We soon expect to see the day when CAE fatigue life prediction for rubber components is regarded as obligatory, given the risk and cost avoided with “right the first time” engineering.

Congratulations to the Stellantis team on this impressive success!

 Fatigue Life (block) demonstrating the accuracy of the CAE Virtual Simulation compared to a physical test

Citation: Elango, C., Pandi, S.K., Mahadule, R.N., and Zarrin-Ghalami, T., “Fatigue Life Prediction and Correlation of Engine Mount Elastomeric Bushing using A Crack Growth Approach,” SAE Technical Paper 2022-01-0760, 2022, doi:10.4271/2022-01-0760.

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Tire Society Takeaways 2021

Image of a TireThe 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 LogoGM’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.

Maxxis Tires LogoPooya 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.

CEAT LogoVidit 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.

Goodyear LogoTom 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

 

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Is It Validated?

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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