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Jay Fineberg

Publications and source records attributed to Jay Fineberg.

25 records · Page 2Linked to original sources
arXiv2009

The 1/r singularity in weakly nonlinear fracture mechanics

Material failure by crack propagation essentially involves a concentration of large displacement-gradients near a crack's tip, even at scales where no irreversible deformation and energy dissipation occurs. This physical situation provides the motivation for a systematic gradient expansion of general nonlinear elastic constitutive laws that goes beyond the first order displacement-gradient expansion that is the basis for linear elastic fracture mechanics (LEFM). A weakly nonlinear fracture mechanics theory was recently developed by considering displacement-gradients up to second order. The theory predicts that, at scales within a dynamic lengthscale $\ell$ from a crack's tip, significant $\log{r}$ displacements and $1/r$ displacement-gradient contributions arise. Whereas in LEFM the $1/r$ singularity generates an unbalanced force and must be discarded, we show that this singularity not only exists but is {\em necessary} in the weakly nonlinear theory. The theory generates no spurious forces and is consistent with the notion of the autonomy of the near-tip nonlinear region. The J-integral in the weakly nonlinear theory is also shown to be path-independent, taking the same value as the linear elastic J-integral. Thus, the weakly nonlinear theory retains the key tenets of fracture mechanics, while providing excellent quantitative agreement with measurements near the tip of single propagating cracks. As $\ell$ is consistent with lengthscales that appear in crack tip instabilities, we suggest that this theory may serve as a promising starting point for resolving open questions in fracture dynamics.

cond-mat.mtrl-sci↗
arXiv2008

The Breakdown of Linear Elastic Fracture Mechanics near the Tip of a Rapid Crack

We present high resolution measurements of the displacement and strain fields near the tip of a dynamic (Mode I) crack. The experiments are performed on polyacrylamide gels, brittle elastomers whose fracture dynamics mirror those of typical brittle amorphous materials. Over a wide range of propagation velocities ($0.2-0.8c_s$), we compare linear elastic fracture mechanics (LEFM) to the measured near-tip fields. We find that, sufficiently near the tip, the measured stress intensity factor appears to be non-unique, the crack tip significantly deviates from its predicted parabolic form, and the strains ahead of the tip are more singular than the $r^{-1/2}$ divergence predicted by LEFM. These results show how LEFM breaks down as the crack tip is approached.

cond-mat.mtrl-sci↗
arXiv2008

Weakly Nonlinear Theory of Dynamic Fracture

The common approach to crack dynamics, linear elastic fracture mechanics (LEFM), assumes infinitesimal strains and predicts a $r^{-1/2}$ strain divergence at a crack tip. We extend this framework by deriving a weakly nonlinear fracture mechanics theory incorporating the leading nonlinear elastic corrections that must occur at high strains. This yields strain contributions "more-divergent" than $r^{-1/2}$ at a finite distance from the tip and logarithmic corrections to the parabolic crack tip opening displacement. In addition, a dynamic length-scale, associated with the nonlinear elastic zone, emerges naturally. The theory provides excellent agreement with recent near-tip measurements that can not be described in the LEFM framework.

cond-mat.mtrl-sci↗
arXiv2006

Oscillations in Rapid Fracture

Experiments of pure tensile fracture in brittle gels reveal a new dynamic oscillatory instability whose onset occurs at a critical velocity, Vc = 0.87 Cs, where Cs is the shear wave speed. Until Vc crack dynamics are well described by linear elastic fracture mechanics (LEFM). These extreme speeds are obtained by suppression of the micro-branching instability, which occurs when sample thicknesses are made comparable to the minimum micro-branch width. The wavelength of these sinusoidal oscillations is independent of the sample dimensions, thereby suggesting that a new intrinsic scale exists that is unrelated to LEFM.

cond-mat.mtrl-sci↗
arXiv2006

Experimental Study of Parametric Autoresonance in Faraday Waves

The excitation of large amplitude nonlinear waves is achieved via parametric autoresonance of Faraday waves. We experimentally demonstrate that phase locking to low amplitude driving can generate persistent high-amplitude growth of nonlinear waves in a dissipative system. The experiments presented are in excellent agreement with theory.

physics.flu-dyn↗
arXiv2006

Crack-Like Processes Governing the Onset of Frictional Slip

We perform real-time measurements of the net contact area between two blocks of like material at the onset of frictional slip. We show that the process of interface detachment, which immediately precedes the inception of frictional sliding, is governed by three different types of detachment fronts. These crack-like detachment fronts differ by both their propagation velocities and by the amount of net contact surface reduction caused by their passage. The most rapid fronts propagate at intersonic velocities but generate a negligible reduction in contact area across the interface. Sub-Rayleigh fronts are crack-like modes which propagate at velocities up to the Rayleigh wave speed, VR, and give rise to an approximate 10% reduction in net contact area. The most efficient contact area reduction (~20%) is precipitated by the passage of slow detachment fronts. These fronts propagate at anomalously slow velocities, which are over an order of magnitude lower than VR yet orders of magnitude higher than other characteristic velocity scales such as either slip or loading velocities. Slow fronts are generated, in conjunction with intersonic fronts, by the sudden arrest of sub-Rayleigh fronts. No overall sliding of the interface occurs until either of the slower two fronts traverses the entire interface, and motion at the leading edge of the interface is initiated. Slip at the trailing edge of the interface accompanies the motion of both the slow and sub-Rayleigh fronts. We might expect these modes to be important in both fault nucleation and earthquake dynamics.

cond-mat.mtrl-sci↗