Integrated Durability Solutions for Elastomers

Will the durability of your new rubber product meet the expectations of your customers? 

Do you have a comprehensive capability that fully integrates all of the disciplines required to efficiently achieve a targeted durability spec?

Your engineers use finite element analysis (FEA) to model the elastomer component in the complex geometry and loading cycle for the desired product application.  One traditional approach to predicting durability is to develop a rough estimate of lifetime by looking at maximum principal strain or stress in relation to strain-life or stress-life fatigue curves obtained for the material using lab specimens in simple tension.  The difficulties and uncertainties with this method were discussed in a recent blog post.

 

A modern approach to elastomer durability is to use the Endurica CL™ durability solver for FEA.  This software uses rubber fracture mechanics principles and critical plane analysis to calculate the fatigue lifetime – which is the number of times the complex deformation cycle can be repeated before failure – for every element of the model.  This provides engineers with the ability to view lifetime throughout the FEA mesh, allowing them to modify design features or make material changes as needed to resolve short-lifetime areas.

A sound finite element model of the elastomer product in the specified loading situation and fundamental fatigue material parameters from our Fatigue Property Mapping™ testing methods are the two essential inputs to the Endurica CL software.  This is illustrated in the figure below.

The requisite elastomer characterization methods can be conducted by us through our testing services or by you in your laboratory with our testing instruments.  For some companies, consulting projects are a route to taking advantage of the software before deciding to license the unique predictive capabilities.  The following diagram shows how our products and services are integrated.

For companies that are just getting started with implementing our durability solutions, the following is a typical testing services and consulting project:

  1. We use our Fatigue Property Mapping™ testing methods, through our collaboration with Axel Products Physical Testing Services, to characterize the properties of cured sheets of rubber compounds sent to us by the client. The minimum requirements for fatigue modeling are crack precursor size and crack growth rate law, and these are quantified within our Core Fatigue Module.  Special effects like strain-induced crystallization and aging/degradation are accounted for using other testing modules when applicable.
  2. The client sends us the output files from their finite element analysis (FEA) of their elastomer part design for the deformation of their complex loading cycle. It is common for the goal to be a comparison of either two designs, two distinct loading profiles, two different rubber compounds, or combinations of these variations.  Our software is fully compatible with Abaqus™, ANSYS™, and MSC Marc™, so the simulations can be conducted on any of these FEA platforms.  In some situations where a client does not have their own FEA capabilities, one of Endurica’s engineers will set up the models and perform the analyses instead.
  3. The fatigue parameters and FEA model are inputted to Endurica CL fatigue solver to calculate values of the fatigue lifetime for every element of the model. The lifetime results are then mapped back onto the finite element mesh in Abaqus, ANSYS, or MSC Marc so that the problem areas (short lifetime regions) within the geometry can be highlighted.
  4. We review the results with the client and discuss any opportunities for improving the fatigue performance through design and material changes.

Advanced implementors of our durability solutions have licensed the Endurica CL software and are using our rubber characterization methods in their laboratories on a routine basis, with instruments provided through our partnership with Coesfeld GmbH & Co. (Germany).  One recently publicized example of a company using the Endurica approach to a very high degree is Tenneco Inc., which you can read about here.

We want to help you #GetDurabilityRight, so please contact me at cgrobertson@endurica.com if you would like to know more about how Endurica’s modern integrated durability solutions for elastomers can help enable a product development path that is faster, less expensive, and more confident.

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Tire Society 2017 – Best Question

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

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

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

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

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

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

ObjectivityTable

 

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Durability Analysis in CAE: panel discussion of metals vs. polymers at the SAE World Congress

The relationship between crack nucleation and fracture mechanics experiments for polymers was first documented in 1964 by Gent, Lindley and Thomas (Journal of Applied Polymer Science, 8, 455, 1964.) 

Some weeks ago, I attended the WCX 2017 SAE World Congress and Exhibition, where a Technical Expert Panel Discussion on the topic of Durability Analysis in CAE was held.  The panel was moderated by Yung-Li Lee (FCA US LLC), and included topic experts Abolhassan Khosrovaneh (General Motors LLC), Xuming Su (Ford Motor Co., Ltd.), and Efthimio Duni (FCA EMEA). The discussion was excellent and wide ranging, owing both to the panelists, and also to the audience, which (judging by the high engagement) was very well versed with the core of the topic, as well as its frontiers. I will not attempt to give a complete summary of the event, but I do want to highlight a memorable discussion thread, and to offer a few thoughts.

I do not know who raised the topic.  It could have been a doctoral student or young professional.  Clearly, it was a person wanting to align his own efforts well relative to larger industry trends.  He started out with the observation that the classical crack nucleation methods (in which fatigue behavior is defined by a stress-life or strain-life curve) are quite popular in the automotive sector for analyzing fatigue of metals.  He also observed that modern tools for rubber take a different approach based upon a fracture mechanics method (in which fatigue behavior is defined by a crack growth rate curve). He then asked (I’m paraphrasing from memory here):

  • Which method (nucleation vs. fracture mechanics) is preferred for analysis of polymers?
  • Should we try to unify all testing and analysis efforts for metals and polymers under the same method?

The panelists made several points in responding to this prompt. They started with the point that differences in methodology may be hard to avoid, if only because metals and polymers are so different in composition, molecular structure, and microstructure.  Of course, it is possible to use fracture mechanical methods with metals, although there are some limitations implied by the granular crystalline structure of metals when cracks are very small.  Likewise, it is also possible to use stress-life methods with polymers, although certain aspects of the material behavior may be incompatible with the usual procedures, leading to questionable results.  From a practical standpoint, it would be quite difficult to change the methods used by the industry for metal fatigue analysis – the methods are quite mature at this point, and they have been implemented and validated across so many codes and projects that it is hard to imagine what could be gained by making a change.  For polymers, CAE durability methods are newer, and we should use what works.

There is a final point that I believe will ultimately define how this all plays out.  It is that 1) fatigue analysis for polymers is usually driven by multiple “special effects”, and that 2) the economics of the testing required to characterize these effects scales very differently between the two approaches.

Let me illustrate with a typical example:  we have a Natural Rubber compound used in a high temperature application, for an extended time, under nonrelaxing loads.  Let’s compare our options:

 

Option 1

Stress-Life Method

Option 2

Fracture Mechanics + Critical Plane Method

To use the stress-life method, we will need to develop curves that give the effect of 4 parameters on the fatigue life: 1) strain amplitude, 2) mean strain, 3) temperature, and 4) ageing.  The experiment is a simple cycle-until-rupture procedure, with one test specimen consumed per operating condition tested.

 

Let’s assume that we measure each of the four parameters at only 3 levels, and that we will require 3 replicates of each experiment.  The total number of fatigue experiments we need is therefore:

 

N = 3 amplitudes x 3 means x 3 temperatures x 3 ageing conditions x 3 replicates = 35 = 243 fatigue to failure tests

 

With the fracture mechanics method, a single run of the experiment solicits the crack at many different operating conditions, enabling observation of the crack growth rate at each condition.  Using Endurica’s standard testing modules, the example testing program (including replication) would require the following procedures:

 

Core module: 9 experiments (amplitude effect)

Nonrelaxing module: 3 experiments (mean effect)

Thermal module: 12 experiments (temperature effect)

Ageing module: 30 experiments (ageing effect)

 

243 tests required 54 tests required

 

In this example, the fracture mechanics method is almost 243/54 = 4.5x more efficient than the stress-life method!  If you need more than 3 levels, or if you have more than 4 key operating parameters, the experimental cost for the stress-life method quickly becomes completely impractical, relative to the fracture mechanics method. Based on these scaling rules, and on the fact that polymers exhibit so many special effects, you can now appreciate why the fracture mechanics method must prevail for polymers.  For metals, the case is less compelling: there aren’t as so many special effects, and the industry testing norms are already well established.

Bottom line: for fatigue of polymers, the economics of testing for ‘special effects’ strongly favors a fracture mechanics approach.  This fact is certain to shape the future development of fatigue life prediction methods for polymers.

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