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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Just Because You Can Doesn’t Mean You Should

When you have an unmet simulation or testing need, should you build or buy the capability?

There are testing instruments and software packages available in the market – which have been improved through years of R&D and quality management – that can meet the needs of a technical team in their product development efforts. Despite these turn-key resources, we sometimes see a company tasking some of its engineers to build their own.

Why does this happen?

Companies hire smart and creative engineers and scientists with advanced degrees to populate their R&D centers. It is common, and even expected in many situations, for a graduate student to create customized equipment or software as a part of a Ph.D. or M.S. research project. Pushing the boundaries of science and technology often requires such development of devices or code. Also, limited research funding in academia can force students to build their own equipment. When young engineers start their industrial careers after graduate school, they carry with them the mindset of building and programming things themselves. These individuals excitedly offer to create when a new analysis or measurement need arises within a company, and managers like to encourage the enthusiasm of their technical staff.

But, even if your sharp engineer can build a DIY testing device or computer program that recreates the state-of-the-art commercial products created by teams of engineers across many years, is this an efficient and strategic use of the engineer’s abilities? If your company makes tires, for example, then shouldn’t you have your smart people focused on making better tires rather than making testing instruments or software?  What are the labor costs, and the opportunity costs, of your highly-skilled engineer building a piece of testing equipment compared to the price of the commercial instrument or relative to the return you could make on an actual improvement to your product? Unless you are in a position to surpass the commercial solution, there is no competitive advantage in the DIY solution. Once you have created your own solution, who will maintain and support it? Will you be able to keep it up to date with advances in technology? Do you have the capabilities and resources to validate your solution more strongly than the market has already validated the commercial solution?

Through my 15 years of experience in materials research and development in the tire and rubber industry, I have seen several pieces of home-built testing equipment collecting dust within companies. Either they were half finished and abandoned or could only be reliably operated by the creator who moved to another department or company.

There can be circumstances where the needed instrument or simulation product is not commercially available. Sometimes the capability exists in the marketplace, but it is not discovered because the maker mindset leads to a halfhearted search. For customized solutions, you may consider working with a vendor to leverage their expertise in creating the required device or program.

If your analysis and testing needs are in the rubber fatigue and lifetime area, please talk to us before you decide to invest in creating your own solutions. Our solutions embody decades of experience. They are the most competitive and strongly validated solutions you can buy. Endurica has specialized finite element analysis software that predicts elastomer durability for complex geometries and loads, and we offer testing instruments for accurately characterizing the fracture mechanics of elastomers through our partnership with Coesfeld GmbH & Co. KG. We can take you quickly to the forefront of fatigue management capabilities.

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Welcome to the Endurica Blog

Welcome to the Endurica blog, written by founder William Mars, Ph.D. These earlier posts (AND MANY MORE) are available on Will’s LinkedIn page:

 

Tire Society 2016: Notes on Advances in Computing Durability –  September 22, 2016

 

 

Strain Crystallization and Durability of Elastomers – August 26, 2016

 

Maximum Principal Stress Damage – August 3, 2016

 

 

Microstructure in Elastomers: Flaw or Feature? – March 26, 2016

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