Session D43: Invited Session: Recent Advances in the Physics of Fractures

Failure of molecules, bones, and the Earth itself

Materials fail by recurring rupture and shearing of interatomic bonds at microscopic, molecular scales, leading to disintegration of matter at macroscale, and a loss of function. In this talk, the state-of-the-art of investigations on failure mechanisms in materials will be presented, in particular focusing on atomistic origin of deformation and fracture, and the relationships between molecular mechanics and macroscale behavior. Simple examples of fracture phenomena are used to illustrate the significance and impact of material failure on our daily lives. Based on case studies, mechanisms of failure of a wide range of materials are discussed, ranging from tectonic plates to rupture of single molecules, and an explanation on how atomistic simulation can be used to complement experimental studies and theory to provide a novel viewpoint in the analysis of complex systems is provided. Biological protein materials are used to illustrate how extraordinary properties are achieved through the utilization of intricate structures where the interplay of weak and strong chemical bonds, size and confinement effects, and hierarchical features play a fundamental role. This leads to a discussion of how even the most robust biological material systems fail, leading to diseases that arise from structural and mechanical alterations at molecular, cellular, and tissue levels. New research directions in the field of materials failure and materials science are discussed and the impact of improving the current understanding of materials failure for applications in nanotechnology, biotechnology, medicine as well as the built environment.   

Fast fracture in slow motion: Dynamic fracture and the effect of near-tip elastic nonlinearities in brittle gels

We present recent results of fracture experiments in poly-acrylamide gels [1]. These gels are soft polymers in which the characteristic sound speeds are on the order of a few meters/sec - thereby slowing down fracture dynamics by 3 orders of magnitude. We first show that the dynamics of rapid cracks are universal; the fracture of gels exhibits characteristic features that are identical with those seen in ``classic'' materials such as glass. These include: \begin{itemize} \item Excellent quantitative agreement with the two different equations of motion for single dynamic cracks predicted by Linear Elastic Fracture Mechanics (LEFM) -- each for different classes of loading conditions. \item The same branching instabilities, localized waves confined to the crack front, and the characteristic structure formed on the resulting fracture surface as observed in ``standard'' amorphous brittle materials, such as soda-lime glass. \end{itemize} We utilize the ``slow motion'' inherent in the fracture of gels to experimentally and theoretically investigate the structure of the deformation fields that surround the tip of highly dynamic cracks. We find that: \begin{itemize} \item The singular fields predicted by LEFM change their structure due to nonlinear elastic effects that dominate the near-tip region [3]. \item This non-linear elastic region provides a quantitative explanation for the oscillatory instability of cracks [2,4] as their speed approaches the Rayleigh wave speed. \end{itemize} These results provide a quantitative first-principles description of how elastic nonlinearity influences the rapid dynamics of a crack. \\[4pt] [1] A. Livne, G. Cohen, and J. Fineberg, Physical Rev. Lett. \textbf{94}, 224301 (2005); T. Goldman, A. Livne, and J. Fineberg, Physical Rev. Lett. \textbf{104}, 11430 (2010).\\[0pt] [2] A. Livne, O. Ben-David, and J. Fineberg, Phys. Rev. Lett.,\textbf{98}, 124301 (2007).\\[0pt] [3] A. Livne, E. Bouchbinder, and J. Fineberg, Phys. Rev. Lett. \textbf{101}, 264301 (2008);. E. Bouchbinder, A. Livne, and J. Fineberg, Phys. Rev. Lett. \textbf{101}, 264302 (2008); A. Livne, E. Bouchbinder, I. Svetlizky, and J. Fineberg, Science \textbf{327}, 1359 (2010).\\[0pt] [4] E. Bouchbinder, Phys. Rev. Lett. \textbf{103}, 164301 (2009).   

Shapes formed by interacting cracks

Brittle failure through multiple cracks occurs in a wide variety of contexts, from microscopic failures in dental enamel and cleaved silicon to geological faults and planetary ice crusts. In each of these situations, with complicated stress geometries and different microscopic mechanisms, pairwise interactions between approaching cracks nonetheless produce characteristically curved fracture paths. We investigate the origins of this widely observed ``en passant'' crack pattern by fracturing a rectangular slab which is notched on each long side and subjected to quasi-static uniaxial strain from the short side. The two cracks propagate along approximately straight paths until they pass each other, after which they curve and release a lens-shaped fragment. We find that, for materials with diverse mechanical properties, each curve has an approximately square-root shape, and that the length of each fragment is twice its width. We are able to explain the origins of this universal shape with a simple geometrical model.   

Fracture Statistics: Universality vs. Nucleation

We reexamine several common assumptions about fracture strength, utilizing large-scale simulations of a fuse network model and applying both renormalization-group and nucleation theory methods. Statistical distributions of fracture strengths are believed to be universal and material independent. The universal Weibull and Gumbel distributions emerge as a consequence of the ``weakest-link hypothesis'' and have been studied in the classical theory of extreme value statistics. These distributions are also the fixed points of a renormalization group (RG) flow. However, the engineering community often ignores the Gumbel distribution and uses the Weibull form almost exclusively to fit experimental data. Further, such fits are often extrapolated beyond the available data to estimate the probability of rare events in a variety of applications ranging from structural reliability to insurance pricing. Our recent studies of the random fuse network model raises doubts about most of these practices. We find that the emergent distribution of fracture strengths is the Gumbel distribution. However, the extremely slow convergence to the universal Gumbel form renders it unusable at least in this case. On the other hand, we show that a non-universal distribution derived by using a Griffiths type nucleation theory (due to Duxbury et al.) converges rapidly even for moderate system sizes. We find that while extrapolating the RG based universal Gumbel distribution is perilous and gives wildly incorrect predictions, the nucleation based non-universal results can be extrapolated with confidence. It is entertaining that fracture provides wonderful examples of the statistical mechanics tools developed to study both continuous as well as abrupt phase transitions.   

Avalanches in crack front propagation

We study avalanches in a model for a planar crack propagating in a disordered medium. Due to long-range interactions, avalanches are formed by a set of spatially disconnected local clusters, the sizes of which are distributed according to a power law. We derive a scaling relation between the local cluster and the global avalanche distributions. For length scales above a crossover length proportional to the Larkin length, the aspect ratio of the local clusters scales with the roughness exponent of the line model. For smaller lengthscales we observe multiscaling in the crack line correlations. Our analysis provides an explanation for experimental results on planar crack avalanches in Plexiglas plates, but the results are applicable also to other systems with long-range interactions such as Barkhausen avalanches in ferromagnetic thin films.