Things that went right in 2020 at Endurica

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

Endurica Software Enhancements

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

Training

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

Testing Instruments

Fatigue Property Mapping Testing Service

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

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

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Does hydrostatic loading cause fatigue damage in rubber?

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

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

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

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

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

where W is the dilatational strain energy density.

 

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

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

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

Figure 2. Computed volume strain – hydrostatic pressure relationship.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

References

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

 

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Keeping Your Secrets

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

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

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

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

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Two Decades of Critical Plane Analysis

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

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

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

 

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

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

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

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

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

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

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

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

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

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

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

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

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Fatigue Property Mapping 2.0

Fatigue Property Mapping Logo

We have just launched a few updates to our Fatigue Property Mapping service offerings.  The changes were:

  1. Addition of the all new Reliability Module for those needing to compute probability of failure in addition to fatigue life. The module gives you Weibull parameters to describe the statistical distribution of crack precursor sizes in your material.
  2. Addition of a pressure-volume test as an optional add-on to the hyperelastic module. Use this add-on when your rubber is loaded under high confinement to the point where its compressibility must be treated more accurately.  If the hydrostatic pressure is more than 5% of the bulk modulus, then this option makes sense.
  3. Split of the original Thermal Module in two components: a Basic Thermal Module and an Advanced Thermal Add-on Module. The Basic Thermal Module provides a dynamic strain sweep to quantify dissipation (for use in computing temperature distribution via FEA) and also provides the temperature sensitivity coefficient on the crack growth rate law.  The advanced module provides thermal transport properties (conductivity, specific heat), thermal expansion coefficient (for computing thermal pre-stresses), and additional data points for the dissipation and crack growth rate laws.
  4. Split of the original Extended Life (Ageing) Module into two parts: a Basic Ageing Module and a Master Curve Module. The basic module includes characterization of unaged and aged samples for stiffness, critical fracture energy, and intrinsic strength.  The oven exposure time and temperature for the aged sample is specified by the client, or can be set by Endurica based upon a client-specified life target.  The Full Master Curve Module gives both the Arrhenius law activation energy and a master curve showing how stiffness, critical fracture energy and intrinsic strength depend on exposure time and temperature.

Most prices have remained the same, except for the Thermal and Ageing modules.  The Thermal and Ageing modules have now been significantly streamlined, so that we now offer service at a lower price.

The new price list and specifications can be found here.

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Conservatism and Tradition in Fatigue Analysis

Slide Rule

Because Endurica’s Critical Plane Analysis is a relatively new approach to fatigue analysis of elastomers (introduced in 2001), new users often ask whether its predictions are conservative.  Ie, does its predictions reliably lean in favor of safety? And is it more or less conservative than the traditional approaches it supplants?

Fatigue analysis for elastomers follows two distinct traditions.  The earliest tradition traces to Sidney Cadwell’s work in 1940 which followed the even earlier ideas of metal fatigue pioneer August Wohler.  This tradition is based on matching up empirical crack nucleation curves to corresponding in-service operating conditions via convenient parameters such as stress or strain.  It is typically the first approach that engineers encounter in their undergraduate training, as it is often effective and relatively simple to apply.  A later tradition, Fracture Mechanics, traces to the post-WWII work of Ronald Rivlin and Alan Thomas in 1953 which extended Griffith’s seminal 1921 work on rupture to elastomers.  In this tradition, the energy requirements for growing a given crack provide the core organizing principle for analysis.  Combined with empirical crack growth rate curves, this approach can make high accuracy life predictions for a very broad range of application scenarios. This approach is typically first encountered in graduate-level engineering programs, and due to somewhat more complicated mathematics, usually requires specialized calculation software to apply it.

There are a few big holes in the Wohler curve approach.  For elastomers, perhaps the biggest limitation is that this approach assumes a priori that damage is associated with the maximum principal stress or strain.  This is sometimes true for simple cases, but not always: 1) strain crystallization is known to produce off-axis cracking not aligned with the principal stress, 2) compression is known to produce cracks on planes of maximum shearing, and 3) out-of-phase multiaxial loading cases do not even possess a unique, well-defined principal direction – the directions vary in time.  It is also well known that Wohler curves for rubber depend strongly on mode of deformation.  Fatigue experiments in simple tension, biaxial tension, simple shear, and simple compression do not simply resolve to a single universal curve, as the Wohler approach takes for granted.  To use this approach conservatively then requires that the most damaging mode of deformation – simple tension – be used as the baseline.

Perhaps the biggest limitation of the traditional Fracture Mechanics approach is that it typically focuses on only one crack at a time.  In fatigue, structures begin with many microscopic cracks distributed randomly throughout.  Most of the fatigue life of the structure is spent growing many small cracks.  Only towards the very end of life do one or a few large cracks finally emerge as worst cases.  True conservatism would mean tracking the growth of all of possible large cracks, and finding out which one(s) grow the fastest.  But traditional fracture mechanics tools are not well adapted for this task.  They require up front assumptions about the location and shape of the worst case crack.  How can you find a worst case without considering many alternatives?

Critical Plane Analysis is simply the idea that a crack could occur anywhere in a structure, and it could occur in any orientation.  It checks all of the possibilities, and it finds the worst ones.  It looks at the specific loading experiences of each individual crack plane that might occur.  It takes account of material behavior like strain crystallization.  It takes account of crack closure conditions.  It takes account of the fracture mechanical behavior of small cracks.  It does not make unwarranted assumptions about the orientation of cracks.  It correctly predicts the orientation of cracks for all modes of deformation.  It is the most exhaustive and conservative fatigue analysis that you can do.

Don’t mistake traditional approaches with the conservative approach.  Critical Plane Analysis is, by definition, the most conservative approach because it doesn’t make any assumptions about crack location or orientation, and because it checks all of the possible ways a crack might occur.

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It Isn’t Durable Unless It’s Reliable

A brand promise of durability (i.e. fitness for service over a suitable period) doesn’t mean much unless it is delivered reliably (i.e. with high consistency).  When automakers provide a 100k mile warranty, for example, it is not enough to simply hit the promised life on average.  Falling short of the promised life should occur only very rarely, if at all.

What effort can be justified in pursuing reliability?  A quick way to estimate economic impact is to look at your product’s warranty adjustment rate.  If your manufacturing contract is worth $10 million dollars / year, and your customer returns 1% of the product for premature failures, then you have an opportunity to save $100k / year by eliminating premature failures.  This is a conservative estimate.  If your early failure rate is notably higher than your competition’s, for example, you may find yourself losing contracts or being forced into price concessions that aren’t sustainable.  A high failure rate may also result in legal liability for losses caused by your part.  In this sense, the total value in achieving reliability can actually approach or even exceed the value of your business!

So in design, consider not only the expected life of the most common crack precursor for your material (half of the samples in your population will have shorter life than this!), but consider also the life of the rare oversized crack precursor that occurs 1 time in 100, or 1 time in 1 million.  We recently launched a new Reliability Module to produce these statistics for exactly this purpose, check it out.  Think of it as a way to put a probability-based “safety factor” on fatigue life predictions.

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Solving the Durability Puzzle

Ever thought about what it takes to deliver the durability you expect from products you use? Durability reflects the combined sum of many decisions made all along the supply chain. What sources to use for raw materials? What dimensions and shape for product features? Are there OEM- or customer-imposed design constraints? What load cases occur in manufacturing, shipping, installation, and operation? Manufacturing processes? OEM-specified qualification and / or regulatory testing requirements? What is the warranty or brand promise? If these decisions are not made well, then durability (as well as cost and weight) will suffer.

The people making these decisions come from many backgrounds.  They are chemists, product engineers, testing engineers, structural analysts.  The big challenge is to organize things so that their contributions all add up to the desired end result: getting durability right, preferably on the first try.  It’s a big challenge because the domain expertise and tools in place today in many organizations were largely built before the science was ready and before the workflows were understood well enough to integrate across disciplines.  This situation can make it quite difficult to solve the durability puzzle.  The pieces don’t all fit together!

  • Oversimplified lab tests whose relationship to actual product use is doubtful
  • Fatigue testing instruments that produce noisy data, or execute with uncontrolled test duration
  • Raw materials suppliers struggling to relate chemistry and process improvements to actual impact on end products
  • Compounders making materials selection decisions based on insufficient / poor information
  • Product engineers missing opportunities to fully leverage material capacity
  • Outdated and inaccurate ‘rule of thumb’ engineering that doesn’t work on new cases
  • Incomplete simulation efforts that fail to forecast or diagnose key durability issues
  • Product qualification tests that under- or over-solicit damage or change failure modes
  • Part suppliers leaving OEMs with too little confidence that durability issues have been handled
  • OEMs and part suppliers struggling to account for actual end-use load cases

Endurica-powered workflows overcome these barriers.  Our training, testing services, testing instruments, and CAE software solutions integrate across disciplines.  Our motto is “Get Durability Right”.

Our classes are geared specifically for your compounders, test engineers, product engineers and analysts.  Your compounder doesn’t need to be a mechanical engineer, but she does need to negotiate the demands on the material.  Your product engineer and your analyst don’t need a PhD in chemistry, but they do need to push for performance that will win for the customer.  Your test engineer needs reliable, productive measurement strategies that get the key information that will power up your materials and product development efforts.  Our classes will pay for themselves many times over when your team confronts the next durability pitfall. 

Our testing services and testing instruments produce a complete picture of what limits durability in your application.  Rubber exhibits many ‘special effects’, and our tests are very useful for quantifying each effect, for building material models, and for solving and diagnosing durability issues.  We partner with leading labs around the world to bring you fast and reliable testing for durability simulation.  We partner with testing instrument maker Coesfeld to bring our protocols directly to your own lab with automated, user-friendly control, measurement and data reduction.  Analysts, designers and materials engineers all need clean, abundant, high-relevance measurements. 

Our software (Endurica CL, Endurica DT, Endurica EIE and fe-safe/Rubber) provides the most complete set of durability analysis capabilities in the world.  Total life, incremental damage, residual life, critical plane analysis, rainflow counting, nonlinear loads mapping, road load signal analysis, stiffness loss co-simulation, self-heating – its all here: documented, supported, validated, with examples and a large user-base.  We support the Abaqus, Ansys and MSC/Marc Finite Element solvers.  Use our software to see how different materials, different geometry, different load / use cases impact durability.  If your materials, product, analysis or testing people can ask the question, chances are that our tools will simulate it and give you new insights. 

Durability doesn’t have to be a difficult puzzle.  It costs way too much when people from different disciplines don’t “speak the same language” and try to go forward with conflicting ideas and tools.  Solve the puzzle by using pieces that fit together.  Get your team speaking Endurican!

Keywords: Compounding, Design, Testing, Analysis, Training

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

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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