Every day, Americans rely on engineered systems such as bridges, buildings and offshore structures that are subject to extreme weather, earthquakes and a range of other conditions. Knowing how materials used in these systems respond to stressors is crucial to creating components that successfully and efficiently do the job.
Engineers rely on mathematical models to predict how the materials they use will react to stressors. However, some “state-of-the-art” models for ductile metals that have been in place for years have done an inadequate job of predicting when and how these materials will eventually fail when exposed to repeated multidirectional permanent deformation, a condition known as multiaxial ratcheting.
Heidi Feigenbaum, professor in NAU’s Department of Mechanical Engineering, recently received a $544,758 grant from the U.S. Department of the Army to develop a mathematical model that will more accurately predict how deformation will accumulate and materials will ultimately fail under cycles of twisting, pulling and pushing. Such a mathematical model has the potential to reduce structure weight, minimize cost, maximize material efficiency—and ultimately ensure that the Army will have safer and more reliable systems.
Feigenbaum will work with NAU professor Constanin Ciocanel and graduate and undergraduate students on the project. She will also collaborate with engineers at the University of California, Davis and the Institute of Thermomechanics, Academy of Sciences in the Czech Republic, who are funded through different sponsors.
Predictive model can be leveraged to improve safety, reliability and material efficiency
“In this work,” said Feigenbaum, “we will develop a means to predict and analyze ratcheting failure in ductile metals such as steel and aluminum, which can be leveraged to improve safety, reliability and material efficiency in a wide variety of structures and systems. This fundamental research will be a major step forward in the field, as despite years of research, predictions made with state-of-the-art models differ dramatically from experimental findings.”
Developing a predictive model is difficult because many variables are involved, such as the load itself, how the material was loaded in the past and whether and how outside influences might affect it.
“When you load a metal but don’t load it too much and then remove the load, it goes back to its original shape. But if you load it too much, it permanently deforms, and that’s called plastic deformation,” Feigenbaum said.
Ratcheting occurs when metals are subject to cyclic plastic deformation.
“Predicting ratcheting is actually very challenging to model mathematically because the deformation depends on how much you load it, how it was previously loaded and what other stresses it experiences in the process,” Feigenbaum said. “Pipes are a good example. If you load one with internal pressure and then twist it and pull on it, it behaves very differently than if you twist it, pull it and then load it with internal pressure. The order and history matter when it comes to permanent deformation of metals.”
Ratcheting can lead to failure in metal systems exposed to extreme weather, earthquakes or repetitive mechanical or thermal conditions. For example, bridges are stressed by everyday heating and cooling. Airplanes are stressed by changing pressure in altitude as they move up and down. Feigenbaum suspects that current predictive models fall short precisely because of the cyclical nature behind ratcheting.
“We think that these models might be just a little off in the initial prediction, but because the loading and stress repeat many times, the prediction’s error increases,” she said. “I don’t mean hundreds or thousands of cycles—I mean dozens. Let’s return to the pipe example. It fills and empties time and time again. Imagine it’s full and an earthquake hits. That earthquake causes the pipe to twist and pull and perhaps elongate over and over, and then it subsides. If our prediction of how the material will react is slightly off but repeats with every cycle, that error grows.”
According to Feigenbaum, because the current models haven’t accurately predicted ratcheting, engineers have overdesigned systems to avoid any risk. That leads to heavier, more expensive and potentially less efficient equipment and structures.
“Imagine I’m a pipe designer. I know ratcheting might occur—an earthquake or some unexpected cyclic loading—so I’ll make my pipe three times thicker than I’m sure it needs to be,” she said. “That’s often the solution: Let’s overdesign to avoid any permanent deformation. We overuse materials because we cannot otherwise ensure safety. If we could predict the safety without that overdesign, we could be much more efficient with our use of materials.”
Feigenbaum’s team plans to use continuum mechanics and thermodynamics principles to investigate ratcheting and come up with a rigorous yet simple model that can be applied to a variety of metals and loading conditions. To do this, the team will address two questions:
- Under repetitive loading that causes permanent deformation, what are the changes in the material state at the continuum level?
- How can these changes in the material be modeled to successfully simulate ratcheting?
Team must achieve a high degree of accuracy to succeed
Feigenbaum knows the team must achieve a high degree of accuracy to accomplish its goal. After they develop the model, they will use data from laboratory experiments to test it. Ciocanel’s lab as well as the Czech team will run the experiments, and Feigenbaum’s team will try to predict the results. When they validate the model’s ability to successfully predict ratcheting, Feigenbaum’s team will implement the mathematical model in software so that engineers can use this model for design.
“We want to prevent failure,” she said. “We want to ensure our engineered systems are safe.”
Feigenbaum joined NAU in 2008. She has active research projects in modeling magnetic shape memory and predicting the behavior of artificial muscles. Her lab, the Feigenbaum Research Group, does work in the areas of continuum mechanics, computational mechanics and smart materials and adaptive structures.