Calibrating Crack Precursor Size in Endurica CL

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, Tc, 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, rc, 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.

 

 

 

 

 


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.

 

 

 

 

 

 



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.

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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.

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: on 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.twitterlinkedinmail

Top 10 Reasons to Celebrate Endurica’s 10-Year Anniversary

In considering ways to capture the contributions and essence of Endurica LLC to celebrate its tenth year of existence – and educating myself some more about the company I joined a little more than a year ago – I decided to put together the following top 10 list.  Enjoy this informative snapshot of Endurica.

10 years of providing software and testing solutions for elastomer applications to #GetDurabilityRight in automotive, tire, aerospace, sealing, defense, consumer products, energy, and medical industries.

9 countries are using Endurica’s elastomer fatigue analysis software products (Endurica CL™, fe-safe/Rubber™, Endurica DT™, and Endurica EIE™) for finite element analysis (FEA).

8 specialized elastomer characterization modules are available in our Fatigue Property Mapping testing services.

7 years ago, the first training course was offered by Endurica. Today there are three courses that are each taught multiple times around the world every year.

6 is the number of full-time teammates working at Endurica LLC.

5 types of integrated durability solutions are offered by Endurica: FEA software, material characterization services, testing instruments, training, and consulting.

4 patents for Endurica’s innovative technology (3 granted plus 1 pending application). 

3 testing instruments are available in the Americas region through our partnership with Coesfeld GmbH & Co. KG (Germany).

2 members of the Endurica team received the Sparks-Thomas Award from the Rubber Division of the American Chemical Society for outstanding contributions and innovations in the field of elastomers.

1st (and only) commercial FEA software to predict when and where cracks will show up in an elastomer product with complex loading and geometry for users of Abaqus™, ANSYS™, and MSC Marc™.twitterlinkedinmail

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.twitterlinkedinmail

Wohler Curves or Fracture Mechanics?

Endurica uses a fracture mechanics based description of rubber’s fatigue behavior, rather than the classical Wohler curve (ie S-N curve) approach.  This is why:

1) Wohler curves in rubber show the combined effects of several nonlinear processes, but they do not easily deconvolve into useful information about the individual processes.  This means that Wohler curve users struggle to trace the causes of fatigue failures any deeper than the single monolithic empirical SN curve.  When the customer or the boss asks why the part is failing, Wohler curve users end up falling back on the old “rubber is mysterious” defense.  Meanwhile, users of critical plane analysis + fracture mechanics are hypothesis testing. They can check what events and what loading directions are most damaging, and what material parameters (crack precursor size, strain crystallization, threshold, crack growth rate law, thermal effects, etc.) can be exploited to gain leverage and solve the issue.

2) Fatigue failure in rubber is often dominated by “special effects”: dependence on strain level, dependence on R ratio, dependence on temperature, dependence on rate, dependence on ageing, etc. The Wohler curve crowd must choose between ignoring/oversimplifying these special effects, or running an experimental matrix that rapidly scales to an infeasibly huge size as more variables are added.  While fracture mechanics users obtain a wealth of information from a single test specimen (one test can probe many different strain levels, temperatures, rates, etc), Wohler curve users obtain 1 data point per tested specimen.  Look in the rubber technical literature and count the number of S-N-curves that are given, relative to the number of fatigue crack growth rate curves.  Google/scholar returns less than 2000 results for “rubber Wohler curve”, and 78700 results for “rubber crack growth curve”.  There is a reason that crack growth rate curves outnumber Wohler curves.

3) SN based methods are not conservative. Wohler curve users end up assuming that a crack will show up perpendicular to a max principal stress or strain direction.  This assumption only works when you have the very simplest loading cases, no compression, and no strain crystallization.  Users of fracture mechanics + critical plane analysis don’t worry about whether they have simple loading, finite straining,  out-of-phase loading, compressive loading, changing principal directions, and/or strain crystallization.  Critical plane analysis checks every possible way a crack might develop and is therefore assured to always find the worst case regardless of detailed mechanisms.

4) Wohler curves are messy. They depend strongly on crack precursor size, which naturally varies specimen-to-specimen, batch-to-batch, and between lab mix and factory processes.  During SN curve testing, the size of the crack is neither measured nor controlled.  This accounts for the extra scatter that is typical in these tests.  In fracture mechanics testing, on the other hand, the crack is measured and controlled, leading to more repeatable and reliable results.  Noisy data means that the Wohler curve crowd has trouble differentiating between material or design options.  Users of fracture mechanics benefit from cleaner results that allow more accurate discrimination with less replication.

A Wohler curve does have one valuable use.  The Wohler curve can be used to calibrate the crack precursor size for a fracture mechanics analysis. It only takes a few data points – not the entire curve, since the crack precursor size does not depend on strain level, or other “special effects” variables.  Our recommended practice is to run a small number of nucleation style tests for this purpose only, then leverage fracture mechanics to characterize the special effects.

The bottom line is that, for purposes of general fatigue life prediction in rubber, the Wohler curve method looses technically and economically to the fracture mechanics + critical plane analysis based method that is used in modern fatigue solvers.twitterlinkedinmail

Fatigue Life Analysis of Free Surfaces

Free surfaces are critical in fatigue analysis because cracks in a physical part tend to form and grow fastest on such surfaces.  Extra care is required when analyzing free surfaces because typical 3D solid finite elements have their worst accuracy at the free surface (gauss points are not located on the free surface, and hydrostatic pressure profile does not conform adequately to element shape function).  Fortunately, the problem is not hard to resolve: free surfaces can easily be skinned with membrane elements.  Membrane elements are specially formulated to produce an exact state of plane stress.

Let’s look at fatigue life predictions that have been computed with a skin of membrane elements, and compare them with predictions computed from the underlying 3D solid elements.

To study the differences in fatigue life calculations, three simple loading cases were used: simple tension, planar tension, and bending. For each case the fatigue life is calculated for both the surface and solid elements.  The results are shown in the table below.

The fatigue life results show that the shortest life always occurred on the free surface. The life for the solid elements varied from 16% to 25% longer than the surface elements. In each case, the critical failure location was on the surface of the part and in the same location for both the solid and surface calculations. The colored contours of fatigue life are shown below for each of the cases.

Figure 1. Fatigue life on simple tension specimen. Isometric view.

 

Figure 2. Fatigue life on planar tension specimen. Cross-section view through the center of the specimen.

 

Figure 3. Fatigue life on bending specimen. Cross-section view through the center of the specimen.

 

Mesh refinement affects the fatigue life results. A mesh refinement study was performed on the bending case. The mesh refinement study consists of the standard mesh model shown above, a coarse mesh model and a fine mesh model. The number of elements in each model triples with each increase in mesh density. The results are shown below.

Figure 4. Mesh Density Analysis on bending specimen.

This mesh density analysis shows that as mesh density increases, the difference in the bulk and surface results decreases. The bulk and surface results converge to a single value. The amount that solid elements on the surface of the part extend into the interior of the part decreases as smaller elements are used. Since the smaller solid elements have a strain history closer to the surface they more closely match the surface element strains and the life results converge to a single value.

Bottom Line:  if you have free surfaces, skin your model with membrane elements for high accuracy results.  Refining your mesh at the surface may help somewhat, but skinning with membranes is far more reliable.

 

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