The Moore Math Marathon Competition!
Friday, May 13, 2016
9:00 a.m. - 2:30 p.m.
The Moore Math Marathon Competition includes both individual and team events, including problems from Algebra I, Geometry, Algebra II, and other interesting math topics.
Mason Helps to Fill Niche in Materials Research
mathematics professor Darren Mason, in collaboration with Philip Eisenlohr of the Max Planck Institute for Iron Research in Germany and Michigan State University engineering professors Tom Bieler and Martin Crimp, has been filling a niche by researching how the material fractures at the microscopic level.When titanium fails—whether on an automobile or an aircraft—the result is usually catastrophic. Albion College
Mason, Albion's Phi Beta Kappa Scholar of the Year, will have the honor of talking about his work in developing a mathematical model used to predict where cracks will occur in titanium when he delivers an address at the International Symposium on Plasticity in January.
Plasticity refers to a material's permanent change in shape when acted on by a force. Mason used a paper clip as an example to demonstrate this phenomenon. If the metal springs back to its original shape after being gently pulled, the material behavior is referred to as elastic. As the strength of the pull increases, and the paper clip stays deformed, then the permanent change in shape is termed plastic.
Using images from a scanning electron microscope, researchers have investigated the relative plastic deformation of adjacent grains in a sample of polycrystalline titanium in tension. When looking at an image magnified to one-30 millionth of an inch, Mason is focused on the unusual behavior observed when these adjacent grains form ledges wherein the material on one side of the horizontal boundary rises above the other like a cliff on a canyon.
“This all started back in 1998 when I was still at Michigan State,” Mason said. “A grant from the Air Force’s Office of Scientific Research funded us for three years. I continued to work with the people at Michigan State after coming to Albion and we were ultimately awarded an additional grant from the National Science Foundation’s Materials World Network program. We finished the initial grant six months ago and we were recently renewed for another three years, so I will be going to Germany [during the summer] for the next three years.
“This summer I worked on what we call a fracture initiation parameter, versions of which have been in the literature for the last 30-40 years, but we have broadened the idea over the last seven years by taking it from the macroscopic parameter to a microscopic parameter,” Mason added. “We ultimately intend to insert the parameter into the computer code that simulates the deformation of the titanium. This summer I investigated the output of the computer simulations of titanium deformation and correlated that with experiments we’ve run on titanium as well as the value of the fracture initiation parameter along grain boundaries. Using the statistical measure that I developed to distinguish between grain boundary populations with ledges and those without has an error rate of less than 3.5 percent—which in our world is pretty good.”
Mason said his future work is to lower the statistical level of error of the fracture initiation parameter used in titanium and broaden the applicability of the fracture initiation parameter concept to include other metals.
“One immediate goal is to apply this research to tantalum in conjunction with related work being done at Sandia National Laboratories,” Mason said.
“I love this research because it is collaborative,” he added. “I love working with people from other universities, other countries, with different areas of expertise because these problems can’t be solved by one person. You’ve got mathematicians talking to computer scientists talking to physicists talking to material scientists talking to people who are experts with microscopes. Each person has their own dialogue and vocabulary that needs to be translated, and there is a certain person who is comfortable walking into a discussion of things they don’t understand. It is a great learning experience for me and it is very rewarding to constantly learn about things I didn’t know.”