Eventually, everything breaks. From small cracks in a dropped phone screen to worn-out foundations of society’s buildings and bridges, all materials will eventually find themselves facing fracture if put under the right amount of stress. When this happens, engineers must rely on their understanding of how fractures form and spread in any given material to mitigate the damage.
In a paper published in Computer Methods in Applied Mechanics and Engineering, CEE professor Oscar Lopez-Pamies presents evidence that the consensus understanding of fracture needs re-evaluation. Specifically, the paper points towards the need for a revitalized approach to predicting nucleation: when and where fractures start.
Historically, the study of fracture has focused on understanding propagation, or how the fractures will grow once they have already formed. In particular, mathematical advances at the turn of the century led to powerful variational phase-field models that can predict how existing fractures spread. This success has led to the use of these models to also attempt to describe fracture nucleation.
Lopez-Pamies’ research shows that while variational phase-field models can accurately describe propagation, their methodology for describing and predicting nucleation produces flawed results.
According to the paper, the biggest issue is the models’ view of a material’s intrinsic strength. While variational phase-field models account for strength as a material property that is dependent on other material properties (the elasticity and the toughness), Lopez-Pamies argues that strength should instead be viewed as an independent material property, one that is described not by a single value, but by an entire surface in stress space.
In a strength surface, the given material is viewed on a 3D grid, with each point representing a unique instance where fracture could occur if stress is introduced. Without the understanding of strength as a surface, researchers have settled for imprecise predictions of nucleation, and as a result have never been able to fully master fracture’s complex impact on their designs. The implications of making this correction, for engineering and beyond, are broad.
“In the context of industrial applications, the work can be utilized to guide the designs and manufacture of any structure, product, or device where fracture is to be avoided or, on the other hand, enhanced,” Lopez-Pamies said. “In the context of medical procedures, the work can be used to guide the development of new procedures for lithotripsy, the breaking of kidney stones, that are more effective, efficient, and safer than those currently in place.”
Looking forward, the first step to achieving such goals will begin with the development of models that can accurately represent the strength surface in their calculations. From there, Lopez-Pamies hopes to refine the process further by investigating other complex phenomena that impact fracture.
“The next step is to extend the approach to account for additional mechanics and physics. For example, in numerous applications, the mechanical loads applied to structures are of a dynamic nature, and the materials used are highly dissipative,” Lopez-Pamies said. “Those problems require accounting for the presence of inertia and for all pertinent mechanisms of dissipation. In other applications, the structures may be subjected to electric and/or magnetic fields. How such fields affect fracture remains to be understood.”
This research was supported with two grants from the National Science Foundation. The full paper, “Classical variational phase field models cannot predict fracture nucleation” can be read here. Co-authors include Duke University Professor John Dolbow, Flatiron Institute Professor Gilles Francfort, and Worcester Polytechnic Institute Professor Christopher Larsen. A companion note, providing simple formulae and specific results, was published in the Journal of Applied Mechanics and can be read here.
Listen to a podcast breaking down the paper on Lopez-Pamies’ website.