Engineering Insights: Dr. Alison McMillan on Modeling Material Fatigue

Fretting is an engineering design challenge for any machine with moving parts. It is a particular issue for components such as bearings, gear teeth, and airfoil root slots, where there is a high load applied and dynamic or vibration contact conditions. Fretting damage occurs when high-pressure conditions are applied to a surface in a region called “edge of bedding,” meaning a region where contact is intermittent.

We recently sat down with Dr. McMillian to learn more about her perspectives on modeling material fatigue. What follows is an excerpt from that interview.

How do various loading conditions, such as tension and compression, affect material response, and how does this understanding guide the development of new models and methodologies?

In materials science, the response of materials to loading conditions is critical. Generally, with loading, materials can be subjected to both pulling and compression. However, with contact loading, the predominant effect is compression. It’s important to note that after compressing, some residual plasticity can induce a degree of tension in the residual stress field, although this is typically minimal. My simulations have shown a limited generation of equivalent plastic strain, which led me to reconsider the strain-hardening models I was using.

In fatigue analysis, the R-factor, which represents the ratio of compression to tension, is crucial. Different loading scenarios can significantly impact fatigue life. My models, especially in contact loading scenarios, suggest an unbalanced R-factor, predominantly in tension. This deviation led me to explore ratcheting effects, which occur in cyclic loading that isn’t fully reversed. Ratcheting can significantly affect material fatigue, especially in materials that are sensitive to such loading histories.

Material models, including the Johnson-Cook model, which describes plasticity based on Mises criteria with hardening behavior, strain-rate dependency and temperature dependency, vary in their approach to hardening rules. These rules often depend on the loading history and strain rate. Exploring various models, I’m considering whether to adopt nonlinear isotropic models or others, considering factors like the Bauschinger effect, which describes how materials’ stress-strain characteristics change due to internal stress distributions.

This theoretical exploration leads to practical considerations. For example, adapting a simple hardness testing machine to experiment with different indenter shapes and material specimens could provide valuable data. By conducting various tests and using reverse engineering optimization with objective functions, it’s possible to fit parameters to the mathematical models in simulation software like Abaqus. This approach could streamline material characterization, potentially offering a more cost-effective method than current practices.

Given these insights, I’ve filed a patent application to protect this novel approach. The goal is to align theoretical predictions with actual material responses under varied loading conditions, thereby enhancing our understanding and characterization of material behavior.

How does integrating mathematical and computational models with traditional engineering methods enhance material understanding, especially regarding fretting fatigue?

My objective is to emphasize the importance of identifying the primary factors contributing to system failures or material degradation. Understanding the root causes of these failures enables more informed decision-making in addressing wear and fatigue issues. Specifically, I’m referring to phenomena like fretting fatigue, where repeated contact and friction between components lead to microstructural damage, manifesting as pitting or surface degradation. It may be beneficial to consider the progression of our understanding of these failures over time in three stages.

1. Traditionally, engineering approaches were predominantly descriptive, focusing on post-mortem analysis of failed components to infer failure modes, and then design to avoid them.
2. However, more modern methodologies go beyond simple observation. In the last 50 years or so, the approach has been to follow a structured testing program, a “pyramid of testing” if you will, where multiple tests are performed at the test coupon, component, assembly, and product levels. The purpose of the multiplicity of testing is to build statistical confidence, because failure through fatigue cannot be predicted with accuracy. The purpose of testing at different levels is to ensure that load application is statistically realistic. Statistical methods, a cornerstone of this approach, are employed to anticipate the likelihood and timing of failures; this is a monster of testing, because the nub of the understanding of fatigue is not known.
3. My work aims to understand that nub better, to fit known science (elasticity theory, and plausible plasticity models that can be validated) around observable facts (geometric features in materials that arise during manufacture or as a natural part), and when fatigue can be understood as a “science” rather than a statistical measurement, build the material specimen tests and validation test program on that scientific basis.

The meme all science is either physics or stamp collecting is attributed to Ernest Rutherford. It might seem disrespectful towards other sciences, but I think the point being made is more subtle. The fundamental point of physics is that the behavior of physical things at one dimensional scale can be predicted or at least understood, based on models of behavior at another scale. Such models generally involve mathematics.

So, in the case of elasticity theory, this is understood based on understanding of chemical bonds (atomic and molecular scale), which informs the concept of crystalline structure (nano scale), which in turn informs the concepts of elastic modulus (macro scale). The mathematics of tensor calculus enables computational modeling of forces and deformations of solid bodies.

The concepts of stress and strain are merely mathematical abstractions, useful as they are. In the same way, understanding of plasticity can be traced back to the atomic or nano scale, but the understanding and modeling steps are more complex. An alloy performs the engineering duty for which is was designed (for example fatigue strength) because the mixing of other elements into the material disrupts the crystalline structure in a beneficial way. The macro scale properties are a consequence of this.

Hence, what I have tried to do is replace simple observation-prediction, which is a “stamp collecting” science action. The “pyramid of testing” concept (multiple tests at coupon, component, assembly, product levels) is also a “stamp collecting” action: each test is a simple observation. There is a mathematical action in the form of statistical analysis, and it does relate one scale to another scale in the sense of coupon through to product, but even a tiny test coupon is macro scale: there is no meaningful physics change, just a complexity change.

By linking macro scale geometry and micro scale geometry features, and then building the modeling based on established principles of elasticity and plasticity (which have their foundation in atomic and nano scale understanding), I am trying to move the science of material fatigue from “stamp collecting” to “physics.” Once it is physics, modeling should become predictive, and testing is then for validation of the models, rather than an exhaustive library of “stamp collections.”

My approach is to integrate mathematical and computational models to predict and analyze failure mechanisms. It involves developing and utilizing computational models grounded in material science principles, such as elasticity and plasticity theories. These models simulate potential stress responses and deformation behaviors under various conditions, essentially providing a mathematical approximation of the material’s performance.

This interdisciplinary approach blends engineering with physics, mathematics, and computer science. It demands a comprehensive understanding of not just the mechanical aspects but also the precision and accuracy inherent in computational simulations. The algorithms and numerical methods employed must be rigorously evaluated for their reliability and validity.

Adopting this multifaceted perspective is substantially beneficial. Relying solely on test and statistics based engineering methods is resource-intensive and costly. By harnessing mathematical and computational techniques, we can reduce the dependency on physical testing, leading to cost-effective and time-efficient solutions. This approach allows for more targeted testing and refined analysis, enhancing the ability to derive insights and make predictions with greater accuracy and less expenditure.

Are you interested in reading more from this interview?   Visit the SIMULIA Community, where we have published Dr. McMillian’s answers to two additional questions:

How does the interplay between porosity and surface roughness in composite materials, especially in additive manufacturing, affect their structural integrity and strain characteristics?

How is SIMULIA’s Abaqus useful in improving my simulation capabilities?

Many thanks to Dr. McMillian for sharing her time and knowledge with us!

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