William V. Mars, Ph.D., P.E.

Dr. Will Mars is an international leader in the failure mechanics of rubber. He is the founder and president of Endurica LLC, and the firm’s products and services are used by leading firms around the world to manage durability. He is the author of the Endurica fatigue life solver, the world’s best-validated fatigue life simulation system for elastomers. Dr. Mars’ career focuses on applying experimental and computational mechanics in pursuit of better-performing rubber products and he has three decades of experience developing testing and simulation methods in the rubber industry. Dr. Mars earned his Honors BSME with Polymer Specialization at the University of Akron, and his MS and Ph.D. degrees at the University of Toledo. He has received several awards for his scientific contributions and innovations including the 2022 Herzlich Medal for outstanding impact and innovation in the tire industry, the 2020 Tibbett’s Award from the Small Business Administration of the United States for excellence in creating cutting-edge technologies, the 2017 Rubber Division ACS Arnold Smith Special Service Award, the 2007 Sparks Thomas award of ACS Rubber Division, and the 1999 Henry Fuchs award of the SAE Fatigue Design & Evaluation committee. Dr. Mars served as the chief editor of Rubber Chemistry and Technology for 10 years and is a former editor of Tire Science and Technology as well. He has over 60 peer-reviewed scientific publications and four patents in the area of elastomer durability.

Tire Society 2017 – Best Question

June 1, 2022September 22, 2017 by William V. Mars, Ph.D., P.E.

Best Question Answer | 56.8 C - Peak temperature | N = 3.8E7 cycles = 131E3 km Cycles to 1 mm Crack

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

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.