Instability in dynamic fracture and the failure of the classical theory of cracks

• Published in: Nature physics 2017-12, Vol.13 (12), p.1186-1190
• Main Authors: Chen, Chih-Hung, Bouchbinder, Eran, Karma, Alain
• Format: Article
• Language: English
• Subjects: 639/301/923/1027; 639/766/119; Atomic; Classical and Continuum Physics; Complex Systems; Condensed Matter Physics; Constraining; Control stability; Crack propagation; Critical velocity; Dynamic stability; Energy; Experiments; Fracture mechanics; Fracture toughness; letter; Mathematical and Computational Physics; Modulus of elasticity; Molecular; Nonlinearity; Optical and Plasma Physics; Physics; Simulation; Stability criteria; Theoretical; Velocity
• ISSN: 1745-2473; 1745-2481
• DOI: 10.1038/nphys4237

Understanding crack formation is important for improving the mechanical performance of materials. A new theory is now presented for the description of cracks propagating at high speeds, with elastic nonlinearity as the underlying principle. Cracks, the major vehicle for material failure 1 , undergo a micro-branching instability at ∼40% of their sonic limiting velocity in three dimensions 2 , 3 , 4 , 5 , 6 . Recent experiments showed that in thin systems cracks accelerate to nearly their limiting velocity without micro-branching, until undergoing an oscillatory instability 7 , 8 . Despite their fundamental importance, these dynamic instabilities are not explained by the classical theory of cracks 1 , which is based on linear elasticity and an extraneous local symmetry criterion to predict crack paths 9 . We develop a two-dimensional theory for predicting arbitrary paths of ultrahigh-speed cracks, which incorporates elastic nonlinearity without extraneous criteria. We show that cracks undergo an oscillatory instability controlled by small-scale, near crack-tip, elastic nonlinearity. This instability occurs above an ultrahigh critical velocity and features an intrinsic wavelength proportional to the ratio of the fracture energy to the elastic modulus, in quantitative agreement with experiments. This ratio emerges as a fundamental scaling length assumed to play no role in the classical theory of cracks, but shown here to strongly influence crack dynamics.