Numerical study of the temperature and porosity effects on the fracture propagation in a 2D network of elastic bonds

This article reports results concerning the fracture of a 2d triangular lattice of atoms linked by springs. The lattice is submitted to controlled strain tests and the influence of both porosity and temperature on failure is investigated. The porosity is found on one hand to decrease the stiffness of the material but on the other hand it increases the deformation sustained prior to failure. Temperature is shown to control the ductility due to the presence of cavities that grow and merge. The rough surfaces resulting from the propagation of the crack exhibit self-affine properties with a roughness exponent $\zeta = 0.59 \pm 0.07$ over a range of length scales which increases with temperature. Large cavities also have rough walls which are found to be fractal with a dimension, $D$, which evolves with the distance from the crack tip. For large distances, $D$ is found to be close to 1.5, and close to 1.0 for cavities just before their coalescence with the main crack

Brittle Crack Roughness in Three-Dimensional Beam Lattices

The roughness exponent is reported in numerical simulations with a three-dimensional elastic beam lattice. Two different types of disorder have been used to generate the breaking thresholds, i.e., distributions with a tail towards either strong or weak beams. Beyond the weak disorder regime a universal exponent of 0.59(1) is obtained. This is within the range 0.4-0.6 reported experimentally for small scale quasi-static fracture, as would be expected for media with a characteristic length scale.Comment: 4 pages and 6 figure

Pinning/depinning of crack fronts in heterogeneous materials

The fatigue fracture surfaces of a metallic alloy, and the stress corrosion fracture surfaces of glass are investigated as a function of crack velocity. It is shown that in both cases, there are two fracture regimes, which have a well defined self-affine signature. At high enough length scales, the universal roughness index 0.78 is recovered. At smaller length scales, the roughness exponent is close to 0.50. The crossover length $\xi_c$ separating these two regimes strongly depends on the material, and exhibits a power-law decrease with the measured crack velocity $\xi_c \propto v^{-\phi}$, with $\phi \simeq 1$. The exponents $\nu$ and $\beta$ characterising the dependence of $\xi_c$ and $v$ upon the pulling force are shown to be close to $\nu \simeq 2$ and $\beta \simeq 2$.Comment: 4 pages, latex, and 4 encapsulated postscript figure

Roughness of tensile crack fronts in heterogenous materials

The dynamics of planar crack fronts in heterogeneous media is studied using a recently proposed stochastic equation of motion that takes into account nonlinear effects. The analysis is carried for a moving front in the quasi-static regime using the Self Consistent Expansion. A continuous dynamical phase transition between a flat phase and a dynamically rough phase, with a roughness exponent $\zeta=1/2$, is found. The rough phase becomes possible due to the destabilization of the linear modes by the nonlinear terms. Taking into account the irreversibility of the crack propagation, we infer that the roughness exponent found in experiments might become history-dependent, and so our result gives a lower bound for $\zeta$.Comment: 7 page

Fracture Roughness Scaling: a case study on planar cracks

Using a multi-resolution technique, we analyze large in-plane fracture fronts moving slowly between two sintered Plexiglas plates. We find that the roughness of the front exhibits two distinct regimes separated by a crossover length scale $\delta^*$. Below $\delta^*$, we observe a multi-affine regime and the measured roughness exponent $\zeta_{\parallel}^{-} = 0.60\pm 0.05$ is in agreement with the coalescence model. Above $\delta^*$, the fronts are mono-affine, characterized by a roughness exponent $\zeta_{\parallel}^{+} = 0.35\pm0.05$, consistent with the fluctuating line model. We relate the crossover length scale to fluctuations in fracture toughness and the stress intensity factor

Dynamical stability of the crack front line

Dynamical stability of the crack front line that propagates between two plates is studied numerically using the simple two-dimensional mass-spring model. It is demonstrated that the straight front line is unstable for low speed while it becomes stable for high speed. For the uniform model, the roughness exponent in the slower speed region is fairly constant around 0.4 and there seems to be a rough-smooth transition at a certain speed. For the inhomogeneous case with quenched randomness, the transition is gradual.Comment: 14 pages, 7 figure

Anomalous roughening of wood fractured surfaces

Scaling properties of wood fractured surfaces are obtained from samples of three different sizes. Two different woods are studied: Norway spruce and Maritime pine. Fracture surfaces are shown to display an anomalous dynamic scaling of the crack roughness. This anomalous scaling behavior involves the existence of two different and independent roughness exponents. We determine the local roughness exponents ${\zeta}_{loc}$ to be 0.87 for spruce and 0.88 for pine. These results are consistent with the conjecture of a universal local roughness exponent. The global roughness exponent is different for both woods, $\zeta$ = 1.60 for spruce and $\zeta$ = 1.35 for pine. We argue that the global roughness exponent $\zeta$ is a good index for material characterization.Comment: 7 two columns pages plus 8 ps figures, uses psfig. To appear in Physical Review

Quantitative AFM analysis of phase separated borosilicate glass surfaces

Phase separated borosilicate glass samples were prepared by applying various heat treatments. Using selective chemical etching we performed AFM measurement on the phase separated glass surfaces. A quantitative roughness analysis allowed us to measure precisely the dependence of the characteristic size of the phase domains on heating time and temperature. The experimental measurements are very well described by the theoretically expected scaling laws. Interdiffusion coefficients and activation energy are estimated from this analysis and are consistent with literature data

Dynamics and Instabilities of Planar Tensile Cracks in Heterogeneous Media

The dynamics of tensile crack fronts restricted to advance in a plane are studied. In an ideal linear elastic medium, a propagating mode along the crack front with a velocity slightly less than the Rayleigh wave velocity, is found to exist. But the dependence of the effective fracture toughness $\Gamma(v)$ on the crack velocity is shown to destabilize the crack front if $(d\Gamma)/(dv)<0$. Short wavelength radiation due to weak random heterogeneities leads to this instability at low velocities. The implications of these results for the crack dynamics are discussed.Comment: 12 page