Research activity
Speed selection in dynamic fractures
Cracks propagate at speeds between 30-70% of the Rayleigh speed, the speed of surface sound waves. Elastodynamic continuum theory however predicts a terminal crack speed of exactly the Rayleigh speed, leading to a quite large mismatch between the two. Understanding this discrepancy has been the subject of extended research activity.
Our work has shown that a very basic mechanism of dissipation is wave emission at the crack tip at all crack speeds, a common experimental phenomenon which is however missing from the elastodynamic continuum theory. As a consequence, only part of the energy delivered to the crack tip is used as fracture energy, the rest being radiated into waves.
At some crack speeds, waves emitted from the crack tip propagate at the same speed of the crack, leading to resonances. This translates into more energy being radiated as waves, and hence leads to a selection mechanism for crack speeds. This description can be made independent of the particular macroscopic set-up (loading conditions, geometry), by introducing an efficiency function which only depends on the material and properly describes the acoustic emission for planar cracks.
For non-planar cracks terminal crack speeds are much lower than the planar case. However, the averall variation of the terminal crack speed with the loading energy resembles the planar case, suggesting the mechanism still remains the same.
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Fig 1: Efficiency as a function of crack speed for a planar crack in a fcc lattice. The efficiency provides the fraction of the total available energy which is used to create new fracture surface, the rest being radiated into acoustic waves. Its speed dependence is a consequence of the coupling between crack velocity and acoustic emission. |
Roughness exponent for fracture surfaces
Advancing cracks can generate fracture surfaces characterized by a nonzero roughness exponent. Experiments show that three regimes for the roughness exponent can be found: marginal loadings give rise to logaritmic scalings or, at short length scales (nanometer scales in metal alloys) a value of 0.5, whilst for large length scales the measured value is about 0.8.
The roughness exponent of a surface is an value which describes its scale invariance properties. A nonzero roughness exponent corresponds to an irregular surface: the scale invariance means briefly that irregularity can be found at any scale of observation, and the magnitude of the roughness exponent corresponds to the magnitude of fluctuations of the surface. The higher the value the more irregular the surface is; the lesser the value, the flatter the surface. A surface with a zero roughness exponent corresponds to a flat surface.
Using a three-dimensional model for quasi-static crack advancement we showed that the roughness exponent depends on the magnitude of the loading: low loadings lead to logarithmic roughness and large values to a roughness exponent of 0.5 corresponding to the one found at short length scales. The build-up of the roughness exponent appears to be connected to the development of macroscopic branches. The origin of the 0.8 value of the roughness exponent is unexplained within the limits of this research: however, crack coalescence was indicated to be behind this larger value.
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Fig 2: Example of fractured sample. Colors refer to level of damage and position within the fcc cell. |
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Fig 3: Example of final surface. The roughness exponent for this surface is about 0.5 |
Interested in joining?
Consequences of acoustic emission on crack speed and roughness exponent in brittle dynamic fracture
Andrea Parisi and Robin C. Ball
in "Earthquakes and Acustic Emission", ed. by A. Carpinteri and G. Lacidogna,
Taylor & Francis (2007) pp. 89-94 [PDFormat]Relation between driving energy, crack shape and speed in brittle dynamic fracture
Andrea Parisi and Robin C. Ball
Physical Review B, 72(5) 054101 (2005) [Prepring]Role of surface waves on the relation between crack speed and the work of fracture
Andrea Parisi and Robin C.Ball
Physical Review B, 66(16), 165432 (2002) [Preprint]Roughness of fracture surfaces
A. Parisi, G. Caldarelli, L. Pietronero
Europhysics Letters, 52(3), 304-310 (2000) [Preprint]Self-affine properties of fractures in brittle materials
A. Parisi, G. Caldarelli
Physica A, 280, 161-165 (2000) [PDFormat]