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It might not seem like scraping the top of a cold stick of butter with a knife could be a scientific test, but engineers at MIT say the process is very similar to the “scratch test,” which is perhaps the oldest known way to assess a material’s hardness and strength — or, in scientific language, its resistance to deformation. Using the scraping of butter as a starting point, the engineers launched a study to see if the age-old scratch test could be used to determine a material’s toughness, or how well it resists fracturing after a small crack has already formed. The answer: The scratch test is indeed measuring crack resistance rather than strength and is valid on material samples of any size. This means that engineers now have a simple “new” test for assessing a material’s fracture properties.
“Fracture mechanics has not reached the same level of pervasiveness in most engineering practice as strength theories, and this is due to the fact that it is difficult to determine fracture properties of materials, from soft clay to hard concrete,” says Franz-Josef Ulm, the George Macomber Professor of Civil and Environmental Engineering (CEE) at MIT. “The test which we propose here is just this: a straightforward test for the engineering practice.”
In a paper in Physical Review Letters that appeared online May 20, co-authors Ulm; Pedro Reis, the Esther and Harold E. Edgerton Assistant Professor of Civil and Environmental Engineering and Mechanical Engineering; and CEE graduate student Ange-Therese Akono — who is first author on the paper — describe their research and findings.
They performed laboratory scratch tests on paraffin wax, which is similar to butter but more stable at room temperature, Reis says, and used theory and mathematics to pare the process down to its essential components. They then created a mathematical model of the entire physical “scratch” process, which shows that the area of contact between the scratching implement and the test material is of primary importance in determining whether the scratch test is assessing strength or toughness.
They knew that when measuring a material’s strength, the force required to make a scratch would always increase at the same rate as the contact area (width times depth) of the scratching tool.
But when measuring a material’s toughness, the mechanics are complicated by the energy released when chemical bonds break as the new surfaces are created and a fracture grows. Because of this, the force does not increase at the same rate as the area of contact. Instead, the force exhibits a distinct scaling reminiscent of a fracture process — that is, a wider cut requires more force than a deeper one. (Specifically, the force increases at the same rate as the width times the square root of the depth.)
Back in the lab, the engineers changed the dimensions of the test to see if a wider scratching implement would require more force than a narrow one. It did. And that seemingly minor change in one dimension gave them their answer: The scratch test is assessing a material’s fracture toughness, not its hardness nor strength properties. It assesses the hardness and strength only in cases where the area of contact between the scratching implement and the material is so small that a true indentation is made rather than a scratch. Now, knowing the width and depth of the scratch and the horizontal force, researchers can now determine the fracture toughness of a material.
“The advantage of a scratch test is that it works on both soft and hard materials and on very small samples,” Akono says. “This method enables us to isolate brittle-crack propagation and neglect plastic deformation.”
They confirmed their findings with additional tests on cement paste, limestone and steel.
“You might think that fracture, or how things break, is an old field of study,” Reis says. “But it’s relatively new compared to the tests of a material’s hardness. Now, using the very old method of the scratch test, we have a relatively simple new means for measuring a material’s toughness.”
“The scalability of scratching for different probes and depths will open new venues for the miniaturization of the technique, which will help us understand fracture properties of materials at very small scales,” Ulm says. “We also know — finally — that it takes less effort to make a narrow, deep cut in cold butter than a wide one. And that is science we can use at the dinner table.”