Software | Endurica LLC

The View on ‘22 – The Top 10 Happenings for Endurica in 2022

January 3, 2023December 14, 2022 by William V. Mars, Ph.D., P.E.

Expanded our team! We welcomed 35-year Goodyear veteran Tom Ebbott to our team as Vice President, and at one point we had 3 interns working with us this year. It wasn’t all hard work – we enjoyed our first company canoe trip / picnic in July.
Solved much bigger problems. We set a record this summer for the largest rubber fatigue analysis ever. Ford Motor Company gave us multi-channel recorded road load histories from the full schedule of 144 distinct test track events that they use to qualify a motor mount for durability. We used Endurica EIE to map the load space and generate 3.2 Terabytes of stress-strain history for fatigue analysis. The new Katana multi-threading architecture of our Endurica CL fatigue solver enabled us to process 152k elements through all 15,693,824 timesteps of the schedule. Check out our presentation at RubberCon 23 in Edinborough UK.
Made analysis of block cycles easier. The Endurica CL and DT solvers’ Katana architecture now enables multiple blocks of load history to be specified in a single analysis.
Added a Haigh diagram visualization to the Endurica Viewer. Use it to quickly understand your material’s dependence of fatigue life on mean strain and strain amplitude.
Implemented a channel reduction algorithm to Endurica EIE. It will analyze your multi-channel loading history to check for opportunities to reduce the dimensionality of your analysis through a change of coordinate basis. Often, a 6-channel signal can be reduced to 3, 4 or 5 channels, greatly reducing computational requirements for building the map for EIE’s interpolation process.
Expanded our licensing model to offer local, regional and global options. If your organization uses Endurica at multiple sites around the world, ask us about the advantage of regional or global licenses. These licenses allow any number of users to share a pool of solver threads for maximum flexibility and compute power.
Added an experimental characterization for ozone cracking. Ozone is a trace gas that strongly reacts with some rubbers to produce surface cracking. It limits useful product life, even for loads below the fatigue threshold. Our testing method gives you the parameters you need to set up the ozone attack model in your Endurica CL / DT analyses. Perfect for analysis of tire sidewall endurance.
Were honored when our founder and president, Will Mars, received the Herzlich Medal – the highest award in the tire industry – at the International Tire Exhibition and Conference. This honor is bestowed every other year to recognize an individual whose career and accomplishments have changed the tire industry for the better and left a lasting impact on tire design, development and manufacturing.
Strengthened our documentation. New and experienced users alike will find it easier than ever to find the theory, procedures and examples that will yield rapid success in applying our software workflows. Check out the new sections on Mullins Effect, Ageing, Safety Factor, and Block Cycle analysis.
Celebrated our client’s success. Technetics Group (Pierrelatte, France Maestral® R&D Sealing Laboratory) and Delkor Rail (New South Wales, Australia) shared their Winning on Durability success in case studies.

Use This One Simple Trick to Ensure Rubber Part Durability

June 9, 2022August 11, 2021 by William V. Mars, Ph.D., P.E.

We’ve just added a new output to the Endurica fatigue solver: Safety Factor. This feature makes it simple to focus your analysis on whether cracks have the minimum energy required to grow. Safety Factor is a quick and inexpensive way to identity potential failure locations. It minimizes the number of assumptions you need to defend, and it is backed by hard science. You don’t need to measure or explain the many influences that together determine how fast cracks grow. You don’t need lengthy materials characterization experiments that take days or weeks. You do need to know your material’s Intrinsic Strength T₀ (ie Fatigue Threshold) and its crack precursor size c₀. The test takes about an hour using the Coesfeld Intrinsic Strength Analyser.

The Safety Factor S is computed as the ratio of T₀ to the driving force T on a potential crack precursor. If the value of the Safety Factor S = T₀/T is greater than 1, it indicates the margin by which crack growth is avoided. If S is less than 1, it indicates that crack growth is inevitable. The calculation of the Safety Factor includes a search for the most critical plane, as we do for our full fatigue life computations.

Although the Safety Factor can’t tell you how long a part will endure, it nevertheless does offer great utility. You can make a contour plot showing the locations in your part where the Safety Factor is the lowest. This is a quick and inexpensive way to identity potential failure locations. You can make statements about the reserve capacity of your design that are easy to communicate and understand with a wide audience.

A vibration isolation grommet operating under small displacement

A vibration isolation grommet operating under large displacement

The images above show a vibration isolation grommet operating under small (Safety Factor 2.6) and large displacements (Safety Factor 0.83). Color contours indicate the Endurica-computed Safety Factor, and use the same scale for both images. Large Safety Factors are shown in blue. Safety Factors approaching 1 are shown in red. Safety Factors smaller than 1 are indicated in black. These results show that the grommet can be expected to operate indefinitely under the small displacements, but that large displacements will produce cracks at some point, in the regions colored black.

Durability by Design on Any Budget

June 9, 2022June 7, 2021 by William V. Mars, Ph.D., P.E.

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.

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.

Road Loads to Block Cycle Schedule

June 9, 2022March 12, 2021 by Mark Bauman

Road loads being converted into block cycle schedules through Endurica software Road load signals are notoriously difficult to work with. The signals feature so many different time increments that it becomes too much to directly model efficiently in FEA. It is difficult to tell which portions of the loading do the most damage. Experimental fatigue testing would be too time-consuming and costly to run on the full complex road load signal. For these reasons simplifying road loads into block cycle schedules has become the gold standard for working with road load signals. Experimental testing and FEA modeling are more manageable when using a block cycle schedule instead of the full road load signal. Traditional methods of converting a road load signal to block cycle schedule can often fall short. Endurica recently added a built-in method in the Endurica CL software that uses the power of critical plane analysis and rain-flow counting to automate block cycle creation.

Let us dive into the process of block cycle creation using an example of a bushing and a road load history. The road loading history shown below contains results for loadings in 3 axes over a time history.

Road Load Time History Graph

The first step in creating the block cycle schedule is solving for the strain history over the entire road load history. Fortunately, Endurica EIE comes to the rescue in solving for the long strain history. The road load time history does not need to be modeled directly in FEA. Instead, a map is run in FEA to solve for strain history within the bounds of the road loading. Endurica EIE quickly interpolates the strains from this map to create the full loading strain history. In the animation below the map points solved for in FEA are shown as black dots and the bushing traces out the path of the map.

Endurica EIE quickly interpolating the strains from this map to create the full loading strain history

After the full road load strain history has been solved for in EIE the fatigue life for the road load signal is ready to be analyzed in CL. The fatigue analysis of the entire road load signal gives valuable insight into finding the critical location, developing the block cycle, and allowing the fatigue life of the block schedule to be validated against the fatigue life of the road load. The critical location of the bushing is shown in the image below:

The fatigue analysis of the entire load signal shows the critical location along with an estimated fatigue life

At the bushing critical location, all damaging events on the critical plane are taken into account when creating the block cycle schedule. The events are grouped into different bins categorized by two parameters: the peak CED and R ratio. The analyst remains in control by selecting the number of bins to group into. Each of the bins contains events with similar peak CED and R ratio that falls within the bounds of the bin. Within each bin, a representative cycle is identified that when repeated in the block schedule will contribute at least as much damage as all the various events in the bin. This selection process produces a conservative result that ensures that the block cycle will be at least as damaging as the road load.

Grouping Damaging events into Bins

The bin results from the original history show the number of times each bin is repeated and the total damage from each bin. At this point, the bins that contribute insignificant damage can be safely eliminated from the block cycle schedule to save testing time and complexity without changing the results.

Comparison of Original history to Block Schedule

The simplified block schedule is then modeled to check the fatigue life vs the full road load signal. The results show that the critical location and fatigue life has been accurately maintained in the block schedule.

Road Load vs. Block Cycle Fatigue + Damage Spheres

This automated block cycle creation procedure succeeded in producing a block cycle with the same critical location and very similar fatigue life. The block cycle selection was able to re-create the full road load signal using only three different loading blocks.

Endurica CL automated block cycle creation lets you take the guesswork out of block cycle creation and harness the proven power of Endurica fatigue analysis technology to get durability right.

Endurica 2019 Updates Released

June 15, 2022February 26, 2019 by Jesse D. Suter

Endurica CL

Endurica CL received many improvements over the past year. These improvements cover a wide variety of different aspects of the software:

Reducing Run-time

Our investments in code benchmarking and performance are paying off! We’ve been able to make internal optimizations to the code that reduce analysis run-times by approximately 30%.

HFM and HFO Formatting

To make our output cleaner and more meaningful, small changes have been made to the number formatting in the HFM and HFO files.

All results reported in scientific notation are now formatted in standard form where the leading digit before the decimal point is non-zero (previously the leading digit was always zero). This gives one more significant figure to all the results without increasing the output file size.

Signal compression

The shortest fatigue life for the analysis is now printed to the console and HFM file with six significant figures. Previously, the life was reported with only two significant figures. This change makes it easier to quickly compare two different analyses, especially when the analyses have similar fatigue lives.

New features have been added to Endurica CL to make it easier to process and analyze histories. Using the new COMPRESS_HISTORY output request, you can generate new HFI files containing compressed versions of your original history. The generated history is composed of the rainflow counted cycles from your original history. An optional output parameter allows you to further compress the signal by specifying the minimum percentage of the original damage that should be retained in the new history. When keeping a percentage of the damage, the cycles are sorted from most to least damaging so that the generated history always contains the most damaging cycles and discards the least damaging cycles.

This output request is useful when you want to reduce a long complex history while keeping the important damaging cycles. This can reduce file sizes and simplify experimental testing setups as well as give you a deeper insight into your duty cycle.

Endurica DT

Endurica DT is our incremental fatigue solver. With Endurica CL, your analysis starts at time zero and integrates the given strain history until end-of-life. With Endurica DT, you can start and end at a series of times that you specify. This lets you accumulate many different histories and loading conditions repeatedly until end-of-life.

Endurica DT gives you new ways to control your analyses, and we have been using it over the past year in many applications. For example, fatigue results for laboratory test procedures that involve multiple loading stages (such as FMVSS No. 139 for light vehicle tires, or block cycle schedules for automotive component applications) can be fully simulated using Endurica DT. You can also compute residual life following some scheduled set of load cases.

Endurica DT can also be used to accumulate the actual loads measured on a part in situ. This allows you to create a digital twin that keeps a near real-time record of the part’s current simulated damage state and the part’s remaining fatigue life.

Stiffness Loss Co-Simulation

Endurica DT now includes a stiffness loss co-simulation workflow that allows you to iteratively update the stiffness of your part over a series of time steps, based on the amount of damage occurring in the part. The stiffness loss is computed per element so you will have a gradient where the more damaged regions become softer. Endurica DT computes the current fraction h of stiffness loss based on the stress and strain, and the finite element solver computes the stress and strain based on the current fractions of stiffness loss. The capability accurately predicts the effects of changing mode of control during a fatigue test. For example, stress controlled fatigue tests show shorter life than strain controlled fatigue tests.

Endurica EIE

Endurica EIE, our efficient interpolation engine, quickly generates long, complex histories using a set of precomputed finite element results (i.e. the ‘nonlinear map’). We first launched EIE last year with the ability to interpolate 1-channel and 2-channel problems. We have recently added the ability to interpolate 3-channel problems.

In the example below, EIE was benchmarked with three-channels. Three separate road load signals were computed from a single nonlinear map. With EIE, you don’t need to rerun the finite element model for each history. Instead, EIE interpolates from the nonlinear map, providing the equivalent results with a 60x speed-up in compute time.

Endurica EIE interpolates from the nonlinear map, providing the equivalent results

EIE – Effect of Map Discretization on Interpolation Accuracy

June 15, 2022September 28, 2018 by Jesse D. Suter

Overview

The accuracy of the interpolated results performed by EIE is dependent on the discretization of the map. Specifically, the results will become more accurate as the map’s point density increases. This study uses a simple 2D model to quantify the accuracy of results interpolated from maps with different densities.

Model

A 1 mm x 1 mm rubber 2D plane strain model with two channels is used. The square’s bottom edge is fixed and the top edge is displaced in the x and y directions as shown below. The x displacement corresponds to channel 1 and the y displacement corresponds to channel 2. The working space of the model is defined by the x displacement ranging from 0 mm to 0.8 mm and the y displacement ranging from -0.08 mm to 0.8 mm.

The model is meshed with 100 8-node, quadrilateral, plane strain, hybrid, reduced integration elements (shown below).

History

We define as the benchmark reference solution a history that covers the model’s entire working space with a high density of points. An evenly spaced grid of 128×128 points for a total of 16384 points is used as the history (shown below). It is important that this history is more refined than the maps that we will create to ensure that we are testing all regions of our maps.

These points are used to drive the finite element model and the results are recorded. For this study, we record the three non-zero strain components and the hydrostatic pressure (NE11, NE22, NE12, and HP) for each element at each time point. In summary, there are 4 result components, 100 elements, and 16384 time increments. This set of results is the reference solution since it is solved directly by the finite element model. We will compare this solution to our interpolated results to measure our interpolation accuracy.

Maps

Six maps with different levels of refinement are used to compute interpolated results for our history points. All of the maps structure their points as an evenly spaced grid. The first map starts with two points along each edge. With each additional map, the number of points along each edge is doubled so that the sixth and final map has 64 edge points. The map points for the six maps are shown below.

The map points for these six maps are used to drive the finite element model’s two channels. The strain and hydrostatic pressure results from the FEA solutions are recorded at each map point in a similar way to how the results were recorded for the FEA solution that was driven by the history points. Next, EIE is used six times to interpolate the map point results at each resolution onto the high resolution reference history points.

We now have seven sets of history results: the true set of results and six interpolated sets of results.

Results

To compare our results, we look at the absolute difference between the sets of results. The absolute error is used, opposed to a relative error, since some regions of the model’s working space will give near zero strain and hydrostatic pressure. Division by these near zero values would cause the relative error to spike in those regions.

Since we have 100 elements and 4 components per element, there are a lot of results that could be compared. To focus our investigation, we look at the element and component that gave the maximum error. The figure below shows contour plots for each of the six maps for this worst-case element and component. The component that gave the maximum error was NE12. The title of each of the contour plot also shows the maximum error found for each of the plots.

Error contours for the worst-case element and component. Titles report the maximum log10 error. — Error contours for the worst-case element and component. Titles report the maximum log₁₀ error.

You can see that the error decreases as the map density increases. Also, you can identify the grid pattern in the contour plots since the error gets smaller near the map points.

Plotting the maximum error for each of the maps against the number of map points on a log scale is shown below. The slope of this line is approximately equal to 1 which is expected since a linear local interpolation was used to compute the results.

Maximum error vs the number of points for each of the six maps

Integrated Durability Solutions for Elastomers

June 7, 2022March 16, 2018 by Christopher G. Robertson, Ph.D.

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 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

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.

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.

Durability Solutions for Elastomers

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

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.
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.
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.
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 us at info@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.

Specifying Strain Crystallization Effects for Fatigue Analysis

June 28, 2022November 3, 2017 by Jesse D. Suter

Endurica CL and fe-safe/Rubber provide several material models for defining cyclic crack growth under nonrelaxing conditions. Nonrelaxing cycles occur when the ratio R is greater than zero. R is defined as

where T is the energy release rate (note that T will always be greater than or equal to zero).

The crack growth rate under nonrelaxing conditions is, in general, a function of both T_max and R. For purposes of calculation, it is convenient to define an “equivalent” energy release rate T_eq that gives the same steady state rate of crack growth as the operating condition on the nonrelaxing crack growth curve, but which is instead on the fully relaxing crack growth curve. In other words,

Using this scheme, you can set up models for both amorphous and strain-crystallizing rubbers, depending on your definition of T_eq. Amorphous rubbers follow the well-known Paris model, and strain-crystallizing rubbers follow the Mars-Fatemi model (or you can define a lookup table).

Paris Model (Amorphous):

The Paris model is the simplest to derive, as it does not involve any material parameters. It defines the equivalent energy release rate as

This definition is only suitable for rubbers that do not strain-crystallize.

For strain-crystallizing rubbers, one of the other two models should be used.

Mars-Fatemi Model (Strain-crystallizing):

The Mars-Fatemi model accounts for strain crystallization by treating the power-law slope, F, of the Thomas fatigue crack growth rate law as a function of R, where

The exponential version is more compact, but the polynomial version is more flexible.

By substituting F(R) into the fatigue crack growth rate equations for relaxing and nonrelaxing cases, and doing a bit of algebra, the following relationship is obtained

Lookup Table (Strain-crystallizing):

The most flexible and accurate way to define strain crystallization is via a lookup table. The lookup table takes R as an input and returns x(R) as an output. This function can be defined as the fraction x(R) by which the nonrelaxing crack growth curve is shifted between the fully relaxing crack growth curve (x=0), and the vertical asymptote at T_c (x=1), at a given R.

This can be rearranged into the desired T_eq (T_max,R) form, as follows

Comparisons:

Visualizing the differences between the models helps gain a better understanding of how strain crystallization can affect fatigue performance. Since all of these models can be represented in the same form of T_eq(T_max,R), we show 2-D contour plots of T_eq with R on the x-axis and ∆T on the y-axis. ∆T is used instead of T_max to make it easier to compare back to the simple Paris model.

From the figures above, we see that for the Paris model, the equivalent energy release rate depends only on ∆T. When using this model, changes in R will have no effect on fatigue performance (when ∆T is also held constant).

For strain-crystallizing rubbers, changes in R should influence fatigue performance. This is seen in the figures for the Mars-Fatemi and lookup table models.

The Mars-Fatemi example uses the following parameters:

The lookup table example uses T_c=10.0 kJ/m² and Lindley’s data for unfilled natural rubber (P. B. Lindley, Int. J. Fracture 9, 449 (1973)).

For these models, there is a significant decline in T_eq as R increases. This effect is most pronounced when T_max is much smaller than the critical energy release rate T_c. Also, there is a point where the effect is reversed (around R=0.8 in these examples) and the high R-ratio starts to have a negative effect on fatigue performance.

Implications:

A material’s strain crystallization properties’ impact on fatigue performance under non-relaxing conditions should not be ignored. Whether you are seeking to take advantage of strain-crystallization effects or simply comparing the results of different materials/geometries/loadings, strain-crystallization should be accurately represented in your simulations.

Follow these tips to take advantage of strain crystallization and help ensure your fatigue performance is the best it can be.

Take advantage of Endurica’s material characterization service (the FPM-NR Nonrelaxing Module generates the strain crystallization curve) or use your own in-house testing to create an accurate strain crystallization model of your material (the nonrelaxing procedure is available for the Coesfeld Tear and Fatigue Analyser).
Use output requests like DAMAGE_SPHERE, CEDMINMAX and CEDRAINFLOW to observe R-ratios for your duty cycles.

References

B. Lindley, Int. J. Fracture 9, 449 (1973)

Mars, W. V. “Fatigue life prediction for elastomeric structures.” Rubber chemistry and technology 80, no. 3 (2007): 481-503.

Mars, W. V. “Computed dependence of rubber’s fatigue behavior on strain crystallization.” Rubber Chemistry and Technology 82, no. 1 (2009): 51-61.

Barbash, Kevin P., and William V. Mars. Critical Plane Analysis of Rubber Bushing Durability under Road Loads. No. 2016-01-0393. SAE Technical Paper, 2016.

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

June 1, 2022June 9, 2017 by William V. Mars, Ph.D., P.E.

Two graphs depicting the relationship between cycles and tearing energy. Through these graphs they show a relationship between a facture mechanics experiment and a crack nucleation experiment.

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.