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Two Decades of Critical Plane Analysis

June 2, 2022April 1, 2020 by William V. Mars, Ph.D., P.E.

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).

Getting a Quick Read on Durability with the Intrinsic Strength Analyser

June 9, 2022March 27, 2020 by Christopher G. Robertson, Ph.D.

There is now a one-hour test on a benchtop instrument for the rubber lab to screen materials for long-term fatigue performance. Please continue reading to learn more about this commercialization of a classical elastomer characterization methodology.

Rubber products manufacturers and raw materials suppliers seeking improved materials for next-generation applications depend on lab tests to predict end-use performance. These predictive tests should balance accuracy, relevance, and testing time. The testing time component is particularly challenging when the performance characteristic of interest is fatigue lifetime. The image of traditional fatigue testers chattering along for days or weeks comes to mind for those of us with experience in industrial rubber labs. The time consideration is the reason why tensile stress-strain testing (stretching a material to high strains until failure) is the most common physical test for the fracture behavior of rubber, in clear contrast to the most prevalent application condition for rubber products which is cyclic loading (fatigue) at much lower strains.

Fatigue crack growth is a key element of elastomer behavior that must be determined in order to predict durability, as illustrated below. For example, fatigue crack growth (FCG) testing provides the FCG rate law that is essential for predicting when and where cracks will show up in rubber products using Endurica’s elastomer fatigue software for finite element analysis [https://endurica.com/integrated-durability-solutions-for-elastomers/]. Endurica has developed a finitely scoped, reduced variability measurement approach¹ which is used in our Fatigue Property Mapping testing services and is available on the Coesfeld Tear and Fatigue Analyser (TFA). Our standard FCG measurement protocol takes 20 hours of continuous testing. This testing time is very efficient for characterizing best candidate materials in the development process, but a faster test is needed for narrowing down, for example, 20 initial materials to 5 best candidates or for use in a plant lab to monitor quality of rubber compounding processes.

Key Components of Elastomer Fatigue and Failure

The Intrinsic Strength Analyser (ISA) is a recent addition to the durability testing solutions for elastomers. The ISA was developed through a partnership between Coesfeld GmbH & Co. (Dortmund, Germany) and Endurica LLC (Findlay, OH, USA), and this benchtop instrument employs a testing protocol based on the long-established cutting method of Lake and Yeoh.^3,4 Endurica’s president, Dr. Will Mars, discusses the importance of measuring intrinsic strength (fatigue threshold) in this video on our YouTube channel which also shows some footage of the ISA in operation:

https://www.youtube.com/watch?v=BL92ppsJZfE

The fatigue crack growth curve of rubbery materials is bounded by the fatigue threshold, T₀, on the low tearing energy (T) side and by the critical tearing energy (tear strength), T_c, at the high-T end. This is depicted in the generalized figure below. A streamlined one-hour procedure on the ISA can measure both T₀ and T_c which can then be used to estimate the slope (F) of the intermediate FCG power law response that correlates well with the actual F from rigorous FCG testing using the TFA (see figure). More information about this quick ISA approach to characterizing rubber crack growth behavior for materials development and quality control can be found in the Annual Review 2019 issue of Tire Technology International (open access).²

ISA graph showing Crack Growth Rate compared to tearing energy

The fatigue crack growth slope

The fatigue crack growth slope, F, from the ISA should be considered an approximate value that is useful for comparing the relative FCG behavior of materials. However, the determination of T₀ on the ISA is highly quantitative and the only realistic option for assessing this parameter, since the near-threshold crack growth testing on the TFA needed to define T₀ would take about a month. The implementation areas for the ISA and TFA are compared in the following table. A very conservative approach to product development for elastomer durability is to create a combination of material behavior and component design that places the final operation of the rubber product below the fatigue threshold. If this is your company’s approach to engineering for durability, then the ISA is the testing instrument you need.

Durability Testing Solutions for the Rubber Lab

Crack precursor size is another key characteristic of elastomers that needs to be quantified in order to predict durability. In combination with a standard tensile stress-strain test, the critical tearing energy (T_c) from the ISA can also be used to assess crack precursor size, as we showed recently in an open access publication.⁵

Endurica is the exclusive Americas distributor of the Coesfeld ISA and TFA instruments. Endurica’s efficient and effective testing protocols are provided on these high-quality instruments for the rubber laboratory. To learn more about how to add these testing capabilities to your lab, please contact us at info@endurica.com.

References

J. R. Goossens and W. V. Mars, “Finitely Scoped, High Reliability Fatigue Crack Growth Measurements”, Rubber Chem. Technol. 91, 644 (2018).
C. G. Robertson, R. Stoček, R. Kipscholl, and W. V. Mars, “Characterizing Durability of Rubber for Tires”, Tire Technology International, Annual Review 2019, pp. 78-82.
G. J. Lake and O. H. Yeoh, “Measurement of Rubber Cutting Resistance in the Absence of Friction”, International Journal of Fracture 14, 509 (1978).
C. G. Robertson, R. Stoček, C. Kipscholl, and W. V. Mars, “Characterizing the Intrinsic Strength (Fatigue Threshold) of Natural Rubber/Butadiene Rubber Blends”, Tire Sci. Technol. 47, 292 (2019).
C. G. Robertson, L. B. Tunnicliffe, L. Maciag, M. A. Bauman, K. Miller, C. R. Herd, and W. V. Mars, “Characterizing Distributions of Tensile Strength and Crack Precursor Size to Evaluate Filler Dispersion Effects and Reliability of Rubber”, Polymers 12, 203 (2020).

Fatigue Property Mapping 2.0

May 27, 2022January 19, 2020 by William V. Mars, Ph.D., P.E.

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

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.
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.
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.
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.

Conservatism and Tradition in Fatigue Analysis

June 9, 2022January 19, 2020 by William V. Mars, Ph.D., P.E.

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: i.e., 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.

So This Happened on the Show Floor at IEC2019

September 27, 2022November 20, 2019 by Pauline Glaza

“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

It Isn’t Durable Unless It’s Reliable

June 9, 2022November 5, 2019 by William V. Mars, Ph.D., P.E.

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.

Durability of 3D Printed Elastomer Structures

June 15, 2022October 3, 2019 by Christopher G. Robertson, Ph.D.

If you are involved in 3D printing with elastomers, can you predict the fatigue behavior?

How is product lifetime affected by complex lattice designs with multiaxial stresses, and what is the impact of printing defects?

Scientific literature and social media are abound with amazing examples of the potential for 3D printed articles made from metals, plastics and elastomers for use in many fields including the biomedical area. Researchers at ETH Zürich recently 3D printed a functioning artificial heart made from a silicone material. A picture of the device is shown below, and the story can be viewed elsewhere.^1,2This pioneering work represents a very noteworthy achievement. This research also highlights the importance of understanding elastomer durability in these cutting edge applications, as the silicone heart only survived 3,000 beats or about 30 minutes.

But the material can only keep going for 3,000 beats at this time.

One of the key differences between 3D printing (additive manufacturing) and conventional manufacturing is the ability of 3D printing processes to create complex structures containing open spaces, often lattice-like in nature. Perhaps the most innovative and high profile example of a 3D printed product with lattice construction is the midsole for the Adidas Futurecraft 4D shoe that is created using the Carbon 3D technology.³

a 3D printed product with lattice construction is the midsole for the Adidas Futurecraft 4D shoe that is created using the Carbon 3D technology.

Overall stresses that are relatively modest and unidirectional translate into much higher stress, multiaxial conditions within the struts of a lattice structure like the shoe sole example above. The finite element simulation below illustrates this for a lattice structure undergoing simple compression (thanks to Mark Bauman, engineering analyst at Endurica).

finite element simulation illustrates this for a lattice structure undergoing simple compression

Multiaxial load cases, crack closure considerations, and other complexities that arise in lattice designs and make it impossible to predict fatigue behavior using simplistic approaches such as Wohler / stress(S)-lifetime(N) curves, can be readily handled using the Endurica CL elastomer fatigue solver for Abaqus, MSC Marc, and ANSYS finite element analysis to predict when and where cracks will show up in the structure.

Cracks in an elastomer start out as microscopic precursors that grow due to applied cyclic loading according to a characteristic crack growth rate law for the material.⁴ In combination with critical plane analysis, this rubber fracture mechanics approach is the cornerstone of our Endurica CL software. The crack precursors – also called intrinsic defects or flaws – are especially important to pay attention to in the additive manufacturing of products in which voids or defects can be introduced by the printing process. The Core Module of our Fatigue Property Mapping testing services includes quantification of crack precursor size, and our new Reliability Module characterizes its distribution. The figure below illustrates the clear influence of crack precursor size on tensile strength in a study wherein we intentionally introduced glass microspheres as flaws in the rubber compound.⁵ Fatigue lifetime shows the same strong dependence on flaw size.

the clear influence of crack precursor size on tensile strength in a study wherein we intentionally introduced glass microspheres as flaws in the rubber compound

Endurica has the software, testing solutions, and expertise to help you understand and improve the durability of your 3D printed elastomer applications, so contact us to see how we can help you #GetDurabilityRight in the additive manufacturing world.

References

https://www.sciencealert.com/this-3d-printed-soft-artificial-heart-beats-just-like-a-real-one
https://www.youtube.com/watch?v=YUYNXeHfTdQ
https://www.youtube.com/watch?v=qlomslovAnI
W. V. Mars, “Fatigue life prediction for elastomeric structures”, Rubber Chemistry and Technology 80, 481 (2007), https://doi.org/10.5254/1.3548175.
C. G. Robertson, L. B. Tunnicliffe, L. Maciag, M. A. Bauman, K. Miller, C. R. Herd, and W. V. Mars, “Characterizing Tensile Strength Distribution to Evaluate Filler Dispersion Effects and Reliability of Rubber”, paper presented at the Fall 196^th Technical Meeting of the Rubber Division, American Chemical Society (International Elastomer Conference), Cleveland, OH, October 8-10, 2019.

Solving the Durability Puzzle

June 3, 2022August 8, 2019 by William V. Mars, Ph.D., P.E.

Solve the Durability puzzle with Endurica 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

Calibrating Crack Precursor Size in Endurica CL

June 6, 2022July 22, 2019 by Mark Bauman

Crack precursors exist in all elastomers owing to the heterogeneous microstructure, even before any loads are applied. The size of the typical precursor must be specified as part of the Endurica fatigue analysis workflow. The best practice for finding the precursor size is to leverage both crack growth and crack nucleation experiments to enforce agreement between the nucleation test results and the corresponding simulation-predicted life results. This procedure guarantees that both the crack growth and the crack nucleation experiments add up to an overall consistent story.

Prior to performing the calibration, you will need to have already defined the hyperelastic law, and the fatigue crack growth rate law. Fatigue models used for rubber have the following parameters:

Relationship between tearing energy and crack growth rate
- The parameters needed to define this relationship are obtained through fatigue crack growth experiments. The crack is loaded under a range of tearing energies while tracking growth of the crack. These tests obtain the critical tearing energy, T_c, which is the tearing energy at which the crack reaches end of life failure in one loading. The crack growth rate at critical tearing energy, r_c, and the slope of the curve, F, are determined by fitting a power law to the experimental crack growth and tearing energy.
Threshold
- This is the tearing energy limit T₀ below which cracks do not grow. If you do not specify this parameter, then you will use the Thomas law. If you do specify this parameter, you will use the Lake-Lindley law. The threshold can be measured using an Intrinsic Strength experiment.
Strain Crystallization
- Some rubbers exhibit a strain crystallization behavior that causes an increase of durability under non-relaxing loads. If the duty cycle of your calibration experiment is nonrelaxing, and if you have a strain crystallizing material, then this characterization should be completed before calibrating the precursor size. The strain crystallization effect is measured in the non-relaxing module.
End of life crack size
- This parameter should be set in the material definition prior to calibrating the precursor size. A default value of 1mm is generally adequate, particularly when it turns out that the precursor size is at least 5x smaller than this value. The part is considered to have failed when a crack reaches this size.

The crack nucleation experiment used for the calibration procedure may be made on a material test coupon, or on an actual component. Test coupons are convenient in early development stages as they do not require having a part to test. So long as crack precursor size is controlled by intrinsic features of the compound recipe (and not by the extrinsic features of post-mixing processes), a test coupon is likely to give useful results. There is a risk when using a test coupon: the risk that the precursor size in a manufactured part is actually controlled by some feature of post-mixing process such as factory contamination, part molding, abrasion, etc. This risk can be mitigated by calibrating precursor size on the basis of crack nucleation experiments on the finished part. In the following example, we show the process for calibration based on a finished part. The process for a test coupon is the same, but the model of the part is replaced by a model of the specimen.

To illustrate, take the case of a rubber bumper spring. Its duty cycle consists of compressing the 150 mm long rubber spring by 80 mm. Experiments show a fatigue life of 282,534 cycles for this duty cycle. A finite element analysis of the rubber spring is made to obtain strain history. The rubber spring is shown in the image below at the initial condition, at 50% of the displacement, and at 100% of the displacement during the fatigue duty cycle.

The rubber spring at the initial condition, at 50% of the displacement, and at 100% of the displacement during the fatigue duty cycle

We are now ready to calibrate the as yet unknown precursor size to the known experimental fatigue test result of the spring. The precursor size can be calibrated by calculating the fatigue life for a series of precursor sizes and then interpolating to find the one precursor size that results in the best agreement between fatigue life calculations and the experimental fatigue life. Use the PRECURSORSIZE_CALIBRATION output request in Endurica CL to produce a table of fatigue life vs. crack precursor size. Your output request syntax will look something like this:

**OUTPUT

PRECURSORSIZE_CALIBRATION, NFS=25, FSMIN=1e-2
LIFE

NFS is the number of precursor sizes to evaluate, in this case 25. FSMIN is the smallest precursor size to evaluate, in this case 0.01 mm.

Once you’ve executed the calibration, use the new Endurica Viewer to complete the calibration workflow. It can plot a wide range of Endurica analysis outputs including precursor size calibration. Just open the Endurica output file containing the calibration results and expand the output file contents tree to find the Precursor Size Calibration results. The viewer then plots the computed table of precursor size vs fatigue life.

The viewer plots the computed table of precursor size vs fatigue life

If you click on the plot options in the upper left corner, you can input the target life and the viewer will interpolate the precursor size. In this case, for a life of 282,534 cycles, the corresponding precursor size is 39 microns. Now that the precursor size is calibrated, the spring geometry can be optimized, different loadings analyzed, or entirely different parts can be analyzed using the material model to get fatigue life results that accurately reflect the precursor size that is most representative of the final material in the part. Again, if a part is not available, precursor size can also be calibrated to fatigue results from standard simple tension test specimen.

The calibrated rubber spring FE model with the life result of 282,534 cycles is shown below.

It sounds like magic but it’s really advanced science and technology

June 15, 2022April 29, 2019 by Pauline Glaza

Endurica's simulation calculates the fatigue life of rubber

When people ask me what Endurica does I tell them: You give us a computer file of one full use cycle of your design – be it a tire design or one rotation of a pump that you’re building a seal for – along with a sample of the rubber you’re making the product of and Endurica will tell you when it will break and where. There are many companies who can do that for metals but we’re the only ones who have figured it out for rubber. It all started with our founder’s Ph.D. work in mechanical engineering and his years in tire design. We actually have more clients outside of the U.S. than in, and our non-disclosure agreements don’t allow us to share names but some of the clients who have published technical papers using our software include General Motors, Caterpillar and Tenneco.

I’ve learned that over-engineering seems to be the status quo in the rubber industry. Because Endurica’s methods aren’t as well-known as we would like, many companies do things the way they always have: test the rubber part for a lifetime of use at the most intense conditions to ensure it fails LONG past the time it could ever be used. That build-and-break routine is so embedded in the industry it led to an interesting insight from an engineer who stopped by our booth at a recent conference.

We don’t have time to do it right, but we do have time to do it over.
– 2019 SAE World Congress Event Attendee

It seems the company they worked for budgets for five to seven full development cycles (design, build, test to breaking point. Re-design; build…..) I’m told that in the tire industry each round of this process easily tops $50,000 when you factor in the engineering time, breaks in actual production schedules for samples to be made, plus months in physical testing. It seems that because many do not understand Endurica’s processes and the foundational science/engineering/technology behind it they continue with the accepted norm of “make and break” even though it costs them hundreds of thousands of dollars annually.

To prevent failure how much do YOU plan to fail?

If that is too strong of a question let me ask it this way: How many design cycles do you have in the budget this year? Simulation is a powerful tool in design and if you are designing on computer already, adding Endurica’s methods to your simulations is the next logical step to, as we say, Get Durability Right.

Consider using the same design budget you already have but replace just one “round” of traditional design with the purchase of Endurica’s training and a software license. By adding our software to your simulation design system (Abaqus, ANSYS or MSC/Marc) you can have results within HOURS (not the months of traditional testing) for the durability of each version of your product design. Envision the impact this technology could have on your firm: reduced time to market; greater design flexibility, increased profitability; reduced costs in both engineering and production…

If there was a better way, would you take it?

Endurica does not advocate that you go directly from simulation to production. We simply make it easier for you to do MANY design cycles to get the best design possible before you do actual FEA testing on the best possible option. Maybe it’s time to reconsider your budget for design cycles, and factor in budget money for both the training to thoroughly understand the science behind Endurica’s methods as well as the software which will enable you to have INFINITELY MORE design iterations for the same overall budget. It isn’t magic but it is pretty advanced science and technology. Let’s talk.