Professor Creates New Theories to Determine Lifetime of Materials

Zdenek Bazant

When it comes to structures such as bridges, airplanes, and ships, the probability of failure must not exceed one in a million. The safety factors ensuring this failure probability generally look at two aspects of the structure: the strength and the structural lifetime.

While the strengths and lifetimes of brittle materials such as metals have been well-studied, ensuring sufficiently small failure probability of newer materials termed "quasi-brittle", e.g. concrete and fiber composites, is still unclear and is the subject of research of Zdenek Bazant, McCormick School Professor and Walter P. Murphy Professor of Civil and Environmental Engineering at Northwestern University.

He and his research group have developed a theory to determine the probability distribution of the strength of these materials and now have extended the same theory to determine the probability distribution of the material and structural lifetime. The results have just been published in the Proceedings of the National Academy of Science of the U.S.A.

To determine the probability of the strength of a material, scientists can test many specimens and determine a curve of distribution of the results, called the histogram. But to determine the lifetime of a material is impractical as it would take decades of testing.

"By relating the structural lifetime to a theory of structural strength, we can predict the distribution of lifetime from the tests for strength and tests of crack growth rate," Bazant says.

Bazant and his group also discovered that such a theory is also mathematically analogous to the probability of failure of computer chips due to tunneling currents, and is also relevant to dental fillings. The theory is based on the analysis of atom-sized cracks.

Research into the lifetime of these materials is important; concrete and fiber composites are used in many infrastructure projects, including tall buildings and bridges, as well as in airplanes and ships.

"A theory of this kind will impact many fields," Bazant says.

Bazant hopes to extend this theory to include probabilities of structural fatigue, temperature, and corrosive environments. Bazant, who works with Northwestern's Infrastructure Technology Institute, hopes that his work will someday be taken into account in the specifications of building codes. "Because each civil engineering structure is different, civil engineers need simple code procedures to produce safe designs effectively," he says.

The fundamental theoretical aspects of this work have been supported by the National Science Foundation, the application to composites by Boeing, and the practical applications to concrete structures by the NU Infrastructure Technology Institute. Other authors on the paper include: Bazant's graduate student Jia-Liang Le, and also Martin Bazant, Zdenek's son, a professor of engineering and mathematics at MIT. This is the first paper the father-son team has co-authored.