MAE 298 Seminar: On the Interplay Between Strength and Energetics in the Fracture of Solids - The Brazilian Test, Explained

Abstract: In this talk, I will first review what is presently known from centuries of experimental
observations about the nucleation and propagation of fracture in solids subjected to mechanical
loads. The observations suggest that there are three basic ingredients that any attempt at a
complete macroscopic theory of fracture ought to account for: i) the elasticity of the material; ii)
its strength at large; and iii) its fracture energy. Much of the recent research in the field of
fracture mechanics has been focused on the propagation of existing cracks, with relatively little
attention placed on the importance of strength. Various models that have been developed to
account for both strength and energetics will be discussed, with particular focus on regularized
models of the phase-field type. In the second part of the talk, I will then discuss a prototypical
example, namely the Brazilian test. The Brazilian test has become a standard approach to
indirectly measure the tensile strength of brittle materials with relatively large compressive
strengths. The test is simple to set up and execute, and it readily lends itself to theoretical
analysis. It consists of a circular disk of the material loaded in compression until it fails, typically
via a sudden fracture that splits the specimen in two. While relatively simple to understand, the
test has proven elusive to various models for fracture. This is likely because it represents a
problem of crack nucleation, particularly under a significant degree of compression. What is
perhaps under-appreciated is the extent to which this oversight has permitted for the
development and acceptance of standardized expressions for tensile strength that can be widely
inaccurate. In this talk, I will highlight our recent work that includes a complete quantitative
analysis of where and when fractures nucleate and propagate in Brazilian tests (static and
dynamic) and how to interpret their results appropriately.

Bio: John Dolbow is a professor of mechanical engineering and materials science at Duke
University, where he directs the Duke Computational Mechanics Laboratory. He is also an
associate vice president for research and innovation at Duke. Professor Dolbow received his
bachelor's degree in mechanical engineering from the University of New Hampshire, and his doctorate in
theoretical and applied mechanics from Northwestern. As a faculty member at Duke
University, he holds appointments in mechanical engineering and materials science, civil and
environmental engineering, and mathematics. His research concerns the development of
computational methodologies and models for problems in fracture mechanics. He has received
various accolades for his research, including Young Investigator awards from both the USACM
and the IACM. He has held visiting appointments at Harvard University, the Okinawa Institute
of Science and Technology, and Sandia National Laboratories. He currently serves as the
secretary-general of the International Association for Computational Mechanics.