Rubber Fatigue ≠ Metal Fatigue Part 2: Linear Superposition

Rubber Fatigue DOES NOT EQUAL Metal Fatigue Part 2 Linear Superposition

The load cases to be considered in fatigue analysis can be very lengthy and can involve multiple load axes. Often, load cases are much longer than can be calculated via direct time-domain finite element analysis (FEA).

In metal fatigue analysis, linear superposition is a widely used technique to generate stress-strain history from road loads [1], [2], [3]. When structures behave linearly, this approach is accurate and computationally efficient, allowing the analysis of lengthy load signals. For single axis problems, the finite element (FE) solution for a single unit load case is simply scaled according to the input load history. For multiaxial problems, unit load cases are solved for each of the axes, then scaled and combined according to the input load history.

Due to rubber’s 1) nonlinear material behaviour, 2) nonlinear kinematics, and 3) the possibility of nonlinear contact, linear superposition cannot be applied to rubber fatigue analysis. This article is the second in a series examining how rubber fatigue analysis procedures differ from those used for metal fatigue. Here we present the Endurica EIETM (Endurica Interpolation Engine) solver, which is a tool for the rapid generation of stress-strain histories for fatigue analysis in cases where linear superposition fails.

Nonlinearity figures in the analysis of rubbery materials in several ways including material nonlinearity, kinematic nonlinearity, and contact linearity. Endurica’s EIE solver provides an efficient and accurate method for generating stress-strain history when there is strong nonlinearity.
Fig.1. Nonlinearity figures in the analysis of rubbery materials in several ways including material nonlinearity, kinematic nonlinearity, and contact linearity. Endurica’s EIE solver provides an efficient and accurate method for generating stress-strain history when there is strong nonlinearity.

Brief review of the linear superposition procedure for metals

For linear structures, the relationship between forces [F] and displacements [u] can be written as a matrix multiplication where [k] is the stiffness matrix.

[F] = [k][u]

The associative property of function composition means that multiplying the displacements by a scalar a produces proportionally larger forces.

a[F] = [k](a[u])

The distributive property of addition means that a force system resulting from combined displacements [u] and [v]

[F] = [k][u] +[k][v]

can also be calculated as

[F] = [k]([u] + [v])

Similarly, stress and strain fields can be scaled and combined by linear superposition. Engineers have been using this principle for many years in metal fatigue analysis, particularly for treating multiaxial cases arising from field-recorded load-displacement histories.

The stress and strain fields in a part are assumed to result from a linear combination of unit load cases, where the scale factor for each unit load case is applied to the stress or strain field corresponding to a given input channel.

For example, for the beam shown in Fig.2, if channel 1 is the unit displacement u with magnitude a(t), and channel 2 is another unit displacement v elsewhere in the structure with magnitude β(t) , then the entire history of stress and strain at all points in the beam can be recovered by linear superposition.

Note that the FE solver only needs to produce a single time-independent solution for each unit load case. The time dependence of the solution is obtained entirely through the time variations of the scale factors a(t) and β(t). This extremely efficient method has been used for many years in metal fatigue analysis. It allows rapid analysis of complete road load histories consisting of millions of time steps.

Linear superposition of single load case FE solutions has long been used to generate stress-strain histories from road load histories in metal fatigue analysis.
Fig.2. Linear superposition of single load case FE solutions has long been used to generate stress-strain histories from road load histories in metal fatigue analysis.

Endurica EIETM: load space discretization and interpolation for nonlinear cases

Solving the nonlinear case requires a completely different approach. We wish to retain the advantages of efficiently constructing stress-strain time histories from precomputed FE solutions. Instead of precomputing a single unit load case for each input channel, we precompute a set of load cases from a discretized load space. We call this set a map.

The number of load cases in the map must be sufficient so that we can use interpolation to obtain an reasonable approximation of the nonlinear response at any point within the map. Fig.3 shows a map with two channels defined by x and z displacements. The blue points in the map are precalculated using an FE solver such as Ansys or LS-Dyna following the path traced by the blue line. Once the map is defined, the stress-strain history along the red line can be interpolated from the precomputed solutions in the map.

Endurica EIE discretization map
Fig.3. Two-channel map discretizing a space defined by the x and z displacements. Blue dots represent FE solutions for which the stress-strain fields are precomputed. The blue line represents a solution path, which defines the order in which the solutions are computed and stored in the results database. The red line represents a possible actual displacement history. The stress-strain history for points on the red path is obtained by interpolation from points on the precomputed map.

Endurica EIETM is a general purpose tool for creating and using non-linear maps to generate stress-strain histories for fatigue analysis [4], [5]. EIE is an abbreviation for efficient interpolation engine. EIE provides a simple workflow and powerful utilities for creating and using maps for interpolation. It supports up to six independent input channels.

The entire EIE workflow consists of three main steps. The first step is to create a map. The next step is to specify your history in terms of forces or displacements. Note that any quantity that can be applied as a boundary condition to the FE model can be set up as a channel. The last step is to perform the specified interpolation. The process produces a time history of strain tensor components for each element in your FE model.

The map creation process involves four steps, as shown in Fig.4. First, the number of independent channels that will be used to specify the history must be defined. The map type must also be specified. Several types are available, including a completely customizable map. Grid-based maps are often appropriate for one-, two- and three-dimensional maps. For higher dimensional maps, case vector-based maps are often the most convenient.

Once the map type has been defined, EIE generates solution paths. These consist of enumerated load states that should be applied as boundary conditions to the FE model to generate the map. One or more paths may be generated depending on map type. Each path is called a branch. For each branch, EIE writes a file with the appropriate boundary condition history, which is necessary for the generation of the map. Next, the FE model is set up and executed using EIE’s boundary conditions. Finally, the database of FE results is linked to the corresponding branch in the definition of the map.

At this point the map is complete and ready for interpolation. Note that linear superposition can be implemented as a special case in EIE when unit load case solutions are collected and defined as a map. In general, however, a non-linear map will contain a greater number of solution steps.

 

Steps to specify a map for use by Endurica EIE.
Fig.4. Steps to specify a map for use by Endurica EIETM.

Specifying the load history is as simple as selecting a file containing the time history of each input channel. In the file, each row represents one time step and each column represents an input channel. EIE supports .csv and .rsp formats, both common data formats. Fig.5 shows an example history with  and  displacements. Note that the range of displacements in the history should not exceed the range of the precalculated map. Although interpolated solutions can be quite accurate, extrapolation for non-linear problems can be very risky and inaccurate.

Endurica example of two-channel displacement history for interpolation
Fig.5. Example two-channel displacement history for interpolation.

Once the map and history are specified, interpolation can begin. Endurica EIETM supports multi-threading, meaning that interpolation calculations can be distributed and executed in parallel across available CPUs. This makes interpolating very fast and very scalable to large models and lengthy histories. Note that Endurica EIETM generates large files because it calculates stress and strain tensor components for each time step of each finite element. It is therefore important to ensure that you have sufficient disk space available when running Endurica EIETM.

Comparing linear and non-linear interpolation results for a sway bar under uniaxial loading

As a first example, consider an automotive sway bar link, shown in Fig.7. The sway bar transmits load in a single axial direction. This model uses Ogden’s hyper elastic law, which involves a non-linear relationship between stress and strain. The large deformation solution also involves non-linear kinematics due to the incompressibility of rubber and finite displacements and rotations. To compare the linear and non-linear interpolation methods, we will run the analysis using both: 1) the linear scaling method (where the map consists of a single load case in which we apply one newton of total load in the x-direction to the link and solve for the strain distribution in the part); and 2) the non-linear method (where the map consists of 11 precomputed steps ranging from -10000N to +10000N).

Endurica sway bar analysis area noted by red arrows
Fig.6. Sway bar link under uniaxial loading (left). Axial load history input for strain history interpolation (right).

Figs. 8–10 show the six engineering strain tensor component history results for both the linear superposition procedure (left) and the nonlinear EIE procedure (right). The results are shown for three different locations on the sway bar bushing (highlighted in red). The largest strain component is the 31 shear (orange line). Note that for the linear procedure, a linear increase in the amplitude of the global force results in a linear increase in the strain components. The non-linear procedure produces quite different results. In fact, where the linear solution predicts symmetry of tension and compression loads, the non-linear solution correctly captures asymmetries.

Endurica Sway Bar Analysis linear and nonlinear
Fig.7. Comparison of linear (left) and non-linear (middle) interpolation results for strain tensor components at the location indicated on the right.
Enduria sway bar analysis top area
Fig.8. Comparison of linear (left) and non-linear (middle) interpolation results for strain tensor components at the location indicated on the right.
Endurica sway bar analysis top at edge
Fig.9. Comparison of linear (left) and non-linear (middle) interpolation results for strain tensor components at the location indicated on the right.

As a final comparison, Fig.11 shows the fatigue life calculated using Endurica CLTM. A longer fatigue life is predicted for the non-linearly interpolated case compared to the linearly interpolated case. Note that the fatigue damage is more concentrated in the linear case and more spatially distributed for the non-linear solution.

Endurica sway bar analysis Linear versus Nonlinear
Fig.10. Comparison of fatigue life calculations based on linear (left) and non-linear (right) interpolated strain history.

Endurica EIETMvalidation for a six-channel non-linear interpolation

As a further test of the non-linear interpolation procedure for a six-channel ( forces +  moments) multiaxial load analysis of the gearbox mount shown in Fig.11, the map shown in Fig.12 was defined. This map contained 51 precalculated non-linear FE solutions. The complete loading history to be interpolated is shown in Fig.13. This history was solved in full directly and interpolated from the map using Endurica EIETM.

Endurica Gearbox Mount Analysis
Fig.11. Gearbox mount analysis. All forces and moments (x, y, and z) were applied at the centre of the top rigid mounting plate.
Endurica Six-channel map containing 51 precalculated finite element solutions.
Fig.12. Six-channel map containing 51 precalculated finite element solutions.
Endurica Full six-channel road load history used for validation analysis of gearbox mount.
Fig.13. Full six-channel road load history used for validation analysis of gearbox mount.

The strain tensor histories for the 11, 22 and 12 strain components are compared between the directly solved and interpolated solutions in Fig.14 at the location of the most critical element. A fairly accurate interpolation was obtained with a much shorter run time than the direct finite element analysis of the full history.

Endurica Comparison of EIE-interpolated strain components (blue) v. direct finite element solution (red) at the location of the most critical element.
Fig.14. Comparison of EIE-interpolated strain components (blue) v. direct finite element solution (red) at the location of the most critical element.

The fatigue life of the gearbox mount was calculated with Endurica CLTM using both the EIE-interpolated strain history and the directly solved strain history. The fatigue contours for both cases are shown in Fig.15. The fatigue life for the interpolated history was 7.52E8 and for the directly solve history the fatigue life was 7.87E8. These results indicate a close agreement between the EIE and directly solved cases. Other validation cases were recently published elsewhere (Mars et al 2024).

Endurica comparison of fatigue life calculated from EIE-interpolated strain components (right) and direct finite element solution (left).
Fig.15. Comparison of fatigue life calculated from EIE-interpolated strain components (right) and direct finite element solution (left).

Conclusion

Analysis of rubber components typically involves strong nonlinearities due to material behaviour, finite strain kinematics, and contact. The traditional linear superposition of unit load cases, widely used in metal fatigue analysis, is not effective in such cases. Fortunately, the Endurica EIETM solver can generate strain histories efficiently and accurately in these cases. The EIE tools allow the analysis to precalculate a set of FE solutions for efficient discretization of the load space and accurate interpolation of signals within the load space. With sufficient discretization of the load space, it was shown that quite accurate results can be produced for cases where there are between one and six load input channels.

MORE

This article by Dr. Mars was published in Futurities magazine in Volume 21 No.3 Autumn 2024 issue on pages 34-38 which can be accessed by clicking here. Futurities is published by EnginSoft, a leading technology transfer company, and an Endurica reseller in Italy.

Dr. Mars originally presented this information in Endurica’s Winning on Durability webinar series. To view the webinar click here.

References

[1.] R. W. Landgraf, “Applications of fatigue analyses: transportation”, Fatigue ’87, vol. 3, pp. 1593–1610, 1987

[2.] Moon, Seong-In et al, “Fatigue life evaluation of mechanical components using vibration fatigue analysis technique”, Journal of Mechanical Science and Technology, vol. 25, pp. 631–637, 2011.

[3.] F. A. Conle and C. W. Mousseau, “Using vehicle dynamics simulations and finite-element results to generate fatigue life contours for chassis components”, International Journal of Fatigue, vol. 13(3), pp. 195–205, 1991.

[4.] K. P. Barbash and W. V. Mars, “Critical plane analysis of rubber bushing durability under road loads”, SAE Technical Paper No. 2016-01-0393, 2016.

[5.] W. V. Mars, “Interpolation engine for analysis of time-varying load data signals”. U.S. Patent 9, 645, 041, May 9, 2017.

[6.] W. Mars,  K. Barbash et al, “Durability of Elastomeric Bushings Computed from Track-Recorded Multi-Channel Road Load Input”, SAE Technical Paper No. 2024-01-2253, 2024.

 

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Rubber Fatigue ≠ Metal Fatigue Part 1: Mean Strain Effects

Rubber Fatigue does not equal Metal Fatigue Part 1 Mean Strain Effects
Figure 1. Constant amplitude cycles at three different mean strains.

Rubber and metal are very different materials that exhibit very different behaviors.  Consider the effect of mean strain or stress on the fatigue performance of these materials.  Figure 1 illustrates a few typical constant amplitude strain cycles, each at a different level of mean strain.  If the stress amplitude is equal to the mean stress, we say that we have pulsating tension or fully relaxing tension.  If the mean stress is zero, we say that we have fully reversed tension/compression.  If the minimum stress is always positive, then we have nonrelaxing tension (i.e. always under load).  Nonrelaxing cycles are quite common in applications.  Examples include: pre-loads applied during installation; swaging of a bushing to induce compressive pre-stresses, interference fits, self-stresses occurring due to thermal expansion/contraction; and in tires, shape-memory effects of textile cords.

In metal fatigue analysis, it is customary to define the effect in terms of stress amplitude σa and mean stress σm, relative to the yield stress σy and the ultimate stress σu, as shown in Figure 2.  Below the fatigue threshold stress σ0, indefinite life is predicted. The Haigh (or Goodman)

Figure 2. Haigh diagram (left) and Wohler curves (right) showing mean strain effects on fatigue life for a metal.

diagram (left) maps fatigue life as a function of these parameters [1]. Wohler curves (right) provide similar information.  For metals, a simple rule may be applied universally: increasing mean strain is detrimental fatigue life.  It is also commonly assumed for metals that the critical plane is perpendicular to maximum principal stress direction.

There are many ways that rubber materials differ from metallic materials.  At the atomic scale, rubber is composed of long chain molecules experiencing constant thermal motion while interlinked with a permanent network topology.  This structure permits large, elastic/reversible straining to occur.  Metals could not be more different, existing as individual atoms packed into well-ordered crystals with occasional dislocations or lattice vacancies.  This structure permits only vanishingly small strains before inelastic deformation occurs.  At the meso scale, rubber is typically a composite material containing fillers such as carbon black, silica or clay, as well as other chemical agents.  The mesoscale of a metal is generally described in terms of crystalline grain boundaries and inclusions or voids.  Rubber exhibits many “special effects” that are not seen in metals: rate and temperature dependence, ageing, cyclic softening.  It is unsurprising that analysis methods for rubber differ substantially from those applied for metals.

Rubber’s fatigue performance has a more complex dependence on mean strain. For amorphous (ie non-crystallizing) rubbers, increasing mean strain reduces the fatigue life, as with metals.  But for rubbers that exhibit strain-induced crystallization, mean strain can greatly increase fatigue life, as illustrated in Figure 3.  Fatigue simulations therefore must take account of the strain crystallization effect.

Figure 3. Fatigue tests run in simple tension under constant amplitude show a significant increase in life for Natural Rubber (NR), which strain crystallizes, and a decrease of life for Styrene Butadiene Rubber (SBR) which is amorphous [2].
Mean strain effects are specified in the Endurica fatigue code in terms of fracture mechanical behavior, using the concept of an equivalent fully relaxing tearing energy Teq.  The tearing energy for fully relaxing conditions is said to be equivalent when it produces the same rate of crack growth as the nonrelaxing condition.  For amorphous rubbers, the equivalent R=0 tearing energy Teq is simply the range ΔT of the tearing energy cycle, which can be expressed in terms of the min and max tearing energies Tmin and Tmax, or in terms of R= Tmin / Tmax.  Plugging this rule into the power law crack growth rate function yields the well known Paris law, which predicts faster crack growth for increasing mean strain.  For a strain crystallizing rubber, the equivalent fully relaxing tearing energy can be specified using the Mars-Fatemi law.  In this case, the equivalent fully relaxing tearing energy depends on a function F(R), which specifies the crystallization effect in terms of its influence on the powerlaw slope of the crack growth rate law.  The relationship for amorphous and crystallizing rubbers are summarized in Table 1 [3,4].

Table 1.  Models for computing crack growth rate in amorphous and strain-crystallizing rubbers.

Rubber’s fatigue behavior may be plotted in a Haigh diagram, but the contours can be quite different than for metals.  In metal fatigue analysis, it is assumed that cracks always develop perpendicular to the max principal stress direction. This is not always true for rubber, especially in cases involving strain crystallization and nonrelaxing loads.  For rubber fatigue analysis it is therefore required to use critical plane analysis [5], in which fatigue life is computed for many potential crack orientations, and in which the crack plane with the shortest life is identified as the most critical plane.  Figure 4 shows the dependence of the fatigue life and the critical plane orientation on strain amplitude and mean strain.  A sphere is plotted for each pair of strain amplitude and mean strain coordinates, on which the colors represent fatigue life, and unit normal vectors indicate critical plane orientations.  It can be seen that different combinations of mean strain and strain amplitude can produce a range of crack plane orientations.

Figure 4. Critical plane analysis consists in integrating the crack growth rate law for every possible crack orientation, and identifying the orientation that produces the shortest life (left). Each point in the Haigh diagram (right) is associated with its own critical plane orientation.

The Haigh diagrams for natural rubber (NR) and for styrene butadiene rubber (SBR) are shown in Figure 5.  In these images, red represents short fatigue life, and blue long life.  For natural rubber (on the left), the long-life region of the Haigh diagram exhibits a notable dome-like shape, indicative of a beneficial effect of mean strain under the influence of strain-induced crystallization. In contrast, SBR always exhibits decreased fatigue life as mean strain increases.  Even so, the Haigh diagram for SBR has a nonlinear character associated with the material’s hyperelasticity that is also distinct from a metal.

Figure 5. Haigh diagrams computed for NR (left) and for SBR (right) rubbers.

It should be noted that the strain crystallization effect in rubber depends on temperature.  At colder temperatures, the effect is stronger, and at higher temperatures it is weaker.  Figure 6 compares experimental Haigh diagrams [6] (top) for a crystallizing rubber to computed results (bottom) for three temperatures.

Figure 6. Experimental Haigh diagram [6] for natural rubber at 3 temperatures (top), compared to computed Haigh diagram (bottom). Increasing temperature tends to reduce the beneficial effect of strain crystallization.
In summary, while tensile mean stresses are always detrimental in metals, in rubber they may be either beneficial or harmful, depending on whether the rubber can strain crystallize. The benefits of mean stresses in rubber can be quite strong – sometimes amounting to more than several orders of magnitude. The beneficial effect is stronger at colder temperatures and is reduced at higher temperatures.  Critical Plane Analysis is essential for accurately predicting the effects of strain crystallization in rubber.  Wohler curves, commonly used for metal fatigue analysis, incorrectly assume that the worst-case plane is always normal to the max principal stress direction.  This is not an accurate approach for strain crystallizing rubber under mean strain.  Use the Endurica fatigue solvers to accurately capture these effects when its important to get durability right!

MORE

This article by Dr. Mars was published in Futurities magazine in Volume 21 No.2 Summer 2024 issue on pages 36-38 which can be accessed by clicking here. Futurities is published by EnginSoft, a leading technology transfer company, and an Endurica reseller in Italy.

Dr. Mars originally presented this information in Endurica’s Winning on Durability webinar series. To view the webinar click here.

References

[1] Stephens, R. I., Fatemi, A., Stephens, R. R., & Fuchs, H. O. (2000). Metal fatigue in engineering. John Wiley & Sons.

[2] Ramachandran, Anantharaman, Ross P. Wietharn, Sunil I. Mathew, W. V. Mars, and M. A. Bauman.  (2017) “Critical plane selection under nonrelaxing simple tension with strain crystallization.” In Fall 192nd technical meeting of the ACS Rubber Division, pp. 10-12.

[3] Mars, W. V. (2009). Computed dependence of rubber’s fatigue behavior on strain crystallization. Rubber Chemistry and Technology82(1), 51-61.

[4] Harbour, Ryan J., Ali Fatemi, and Will V. Mars. “Fatigue crack growth of filled rubber under constant and variable amplitude loading conditions.” Fatigue & Fracture of Engineering Materials & Structures 30, no. 7 (2007): 640-652.

[5] Mars, W. V. (2021). Critical Plane Analysis of Rubber. Fatigue Crack Growth in Rubber Materials: Experiments and Modelling, 85-107.

[6] Ruellan, Benoît, J-B. Le Cam, I. Jeanneau, F. Canévet, F. Mortier, and Eric Robin. “Fatigue of natural rubber under different temperatures.” International Journal of Fatigue 124 (2019): 544-557.

 

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2023 – a Year of Magnitude and Direction

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

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

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

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

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

Top 10 Code Developments:

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

 

Testing Hardware

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

 

Applications, Case Studies, Webinars

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

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

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

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The 5-50-500 Rule

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

2 Minute Read | 400 Words

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

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

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

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

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

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Busting Myths About Endurica

Myths vs Facts on Endurica, Test your knowledge about Endurica

True or False? Test your knowledge about Endurica

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

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

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

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

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

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

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

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

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Virtual vs. Physical in 2021 and Beyond

An insight to how Endurica stayed connected during Covid-19, by using Microsoft teams to meet virtually.These days everybody’s talking about whether to meet in person or online.  There are great tools available for online meetings, and these have helped us navigate Covid-19. Like everyone else, Endurica teammates regularly use online meeting technology.  But if there is one thing we learned over the last year, it is that sometimes physical presence really matters. Living and working in isolation is just not healthy in the long run.

The new normal during the pandemic had some benefits that were enabled by the virtual world. Time and energy that used to be consumed by travel were rechanneled into improving our software, testing services, and marketing materials. In our personal lives, we had more opportunities to spend quality time with our immediate families and found more time for fitness activities. We previously talked about our pandemic pivots to bring our training courses online and offer webinars to stay in touch with our existing and potential customers.

But virtual meetings can’t replace the full experience of being together in person.  The face-to-face engagement at a trade show, the serendipitous bumping into a client, the spontaneous discussion of ideas with fellow conference-goers with a shared interest, the rapport building that comes from shared experiences.  We fundamentally need physical connection. A hug, delivered via Zoom, will never feel the same.

The world of 2021 and beyond is hybrid: part virtual, part in-person.  The benefits of the virtual are too great to set aside, and the necessity of the physical is too compelling to neglect.  Both are critical to our future, at home and at work.

So, too, with Endurica’s simulation workflows. It was NEVER Simulation OR Build-and-Break. Even the best simulations are not enough to completely skip physical testing. The virtual approach saves significant time and money in product development and design refinement. It allows you to explore a huge space of compound options and of design features before investment in building and testing prototypes. Our simulations enable you to balance difficult trade-offs. Still, before you head into production, you must complete actual physical testing on your rubber part – the physical world is what counts in the end. It is simulation AND build-and-break that are both needed in concert to #GetDurabilityRight.

Just as a Zoom hug will never replace the real thing, software will never replace the role of physical testing.  But just as online meetings are creating new opportunities and efficiencies, Endurica’s tools position you for unprecedented success when it’s time to test.

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

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Durability by Design on Any Budget

Durability by Design

So, you’ve got a tricky durability problem to solve, a budget, and a deadline.  Let’s look at a helpful framework for sorting which Endurica workflows you need.  In the grid below, each row represents a potential approach you can take.  The approaches are, in order of increasing complexity and cost, the Infinite Life approach, the Safe Life approach, the Damage Tolerant approach, and the Fail Safe approach.

Endurica Durability Workflows

The Infinite Life approach is by far the simplest approach.  Here, we say that damage will not be allowed at all.  All locations in the part must operate, at all times, below the fatigue limit (ie intrinsic strength) of the rubber.  The required material testing is minimal: we need only know the fatigue limit T0 and the crack precursor size c0.  We avoid the question of how long the part may last, and we focus on whether or not we can expect indefinite life.  We report a safety factor S indicating the relative margin (ie S = T0 / T) by which each potential failure location avoids crack development.  When S>1, we predict infinite life.  For S<=1, failure occurs in finite time and we must then go on to the next approach…

In the Safe Life approach, the chief concern is whether or not the part’s estimated finite life is adequate relative to the target life.  The material characterization now becomes more sophisticated.  We must quantify the various “special effects” that govern the crack growth rate law (strain crystallization, temperature, frequency, etc.).  We consider the specific load case(s), then compute and report the number of repeats that the part can endure.  If the estimated worst-case life is greater than the target life then we may say that the design is safe under the assumptions considered.  If not, then we may need to increase the part’s load capacity, or alternatively to decrease the applied loading to a safe level.  In critical situations, we may also consider implementing the next level…

The Damage Tolerant approach acknowledges that, whatever the reasons for damage, the risk of failure always exists and therefore should be actively monitored.  This approach monitors damage development via inspection and via tracking of accrued damage under actual loading history.  A standard nominal load case may be assumed for the purpose of computing a remaining residual life, given the actual loading history to date.  Changes in material properties due to cyclic softening or ageing may also be tracked and considered in computing forecasts of remaining life.

The Fail Safe approach takes for granted that failure is going to occur, and obliges the designer to implement measures that allow for this to happen safely.  This can take the form of a secondary / redundant load path that carries the load once the primary load path has failed.  It can take the form of a sacrificial weak link / “mechanical fuse” that prevents operation beyond safe limits.  It can take the form of a Digital Twin that monitors structural health, senses damage, and requests maintenance when critical damage occurs.

The last three columns of the grid show which Endurica fatigue solver workflows align with each design approach.  The Endurica solvers give you complete coverage of all approaches.  Whether you need a quick Infinite Life analysis of safety factors for a simple part, or deep analysis of Damage Tolerance or Fail Safety, or anything in-between, our solvers have just what you need to get durability right.

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So This Happened on the Show Floor at IEC2019

Convention Floor

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

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

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

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

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

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

 Cost of Qualifying Fatigue Performance | 100 Grand

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Behind the Scenes Tour of Endurica Software Development and QA Practices

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

Automation:

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

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

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

Reliability:

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

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

Repeatability:

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

Traceability:

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

Responsiveness:

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

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

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

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

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

Q: Where is the industry today?

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

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

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

 

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