Scaling and universality in real cracks

Roughness scaling laws for intergranular cracks deviate from self-affine (fractal-like) behavior at length scales related to the polycrystalline microstructure. We consider two versions of the same alloy material with many of the same microstructural length scales but differing in their processing history: one conventional and one grain boundary engineered. The engineered material, processed to contain a high fraction of ''special" grain boundaries, fails more slowly and more isotropically. We present evidence that the difference is determined by processes related to clusters of twin-related grains, shown through analysis of scales of the fracture roughness measured with confocal microscopy and the special grain boundary network determined by electron backscatter diffraction. Above the cluster scale, the fracture roughness exponents in the two materials are nearly indistinguishable (confirming theoretical predictions); below this scale conventional cracks exhibit correlations indicating consistently weak paths for crack propagation, suggesting percolation of ''random" boundaries.

1999

ABSTRACT The long distance roughness of fatigue fracture surfaces of a nickel-based superalloy is reported for two samples of different grain size. Statistical analysis over a wide range of length scales, from a few nanometers to a few millimeters, using scanning electron microscopy and atomic force microscopy allows to obtain accurately the self-affine correlation length.

Europhysics Letters (EPL), 2000

We study the roughness of fracture surfaces of three dimensional samples through numerical simulations of a model for quasi-static cracks known as Born Model. We find for the roughness exponent a value ζ ≃ 0.5 measured for "small length scales" in microfracturing experiments. Our simulations confirm that at small length scales the fracture can be considered as quasi-static. The isotropy of the roughness exponent on the crack surface is also showed. Finally, considering the crack front, we compute the roughness exponents of longitudinal and transverse fluctuations of the crack line (ζ ∼ ζ ⊥ ∼ 0.5). They result in agreement with experimental data, and support the possible application of the model of line depinning in the case of long-range interactions.

Physical Review Letters, 1992

We record the height of the crack surface as a function of position along one-dimensional cuts orthogonal to the crack for six diA'erent brittle materials. We find that the width w of this one-dimensional trace as a function of its length L behaves as w-Lr, where (=0.87(7). This result is in agreement with recent conjectures of a universal roughness exponent g for these materials.

Europhysics Letters (epl), 2010

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.

Physical Review Letters, 2004

Intergranular and transgranular fracture surfaces obtained in a face centered cubic alloy are studied using 3D maps reconstructed by scanning electron microscopy stereo imaging. The roughness exponents measured in the intergranular and transgranular surfaces, respectively, 0:83 0:05 and 0:75 0:05, are in agreement with the universal roughness value of 3D fractures. However, the slightly smaller value related to the transgranular surface could be a consequence of crystallographic transgranular zones disseminated on the surface whose roughness exponent 0:65 0:07 is close to the one usually measured on 2D fractures.

Physical Review Letters, 2006

The self-affine properties of post-mortem fracture surfaces in silica glass and aluminum alloy were investigated through the 2D height-height correlation function. They are observed to exhibit anisotropy. The roughness, dynamic and growth exponents are determined and shown to be the same for the two materials, irrespective of the crack velocity. These exponents are conjectured to be universal.

Fracture of Nano and Engineering Materials and Structures

In this paper the authors present results of in situ observation of crack growth in various materials, at various length scales and under various modes of loading. In order to approach better understanding of the fracture behaviour light microscope (LM) with in-situ recording device, scanning electron microscope (SEM) equipped with a tensile test device and transmission electron microscope (TEM) with a straining holder have been utilized. In situ investigations by light microscopy were carried on pure Cu of bimodal grain size with microcrystalline grains embedded in sub-microcrystalline matrix. For quantitative description of strain field the Digital Image Correlation method was used. As a result of the performed examinations it was found that a crack propagating in a material with bimodal grain size distribution meanders, due to which fracture surface is not flat. This allows presuming that materials with such structure have higher resistance to cracking than materials with homogeneous grain size distribution. In situ SEM fracture studies were performed on the coarse grain Al sample directly in the vacuum chamber of SEM, equipped with tensile test device. The sample with a thickness of 0.2 mm was pre-notched by means of electro polishing. The processes of strain localization, crack initiation and propagation have been investigated with details showing distribution of slip bands. A 316 type stainless steel for the in situ TEM dislocation pile ups against grain boundary studies as an appropriate material having low stacking fault energy has been chosen. An increase of dislocation number in the pile ups as well as a slip of the dislocation in the opposite direction was registered and analyzed in detail. The presented research results show that in situ examinations are useful in revealing phenomena occurring in the crack tip plastic zone. These investigations can be conducted at various length scales, which allows to reveal various phenomena, starting from quantitative description of deformation in case of examinations with use of light microscopy, through SEM examination of slip bands, up to an analysis of individual dislocations behaviour in case of transmission electron microscopy.

The paper focuses on the effective resistance and the near-threshold growth mechanisms in the ferritic-pearlitic and the pure pearlitic steel. The influence of microstructure on the shear-mode fatigue crack growth is divided here into two factors: the crystal lattice type and the presence of different phases. Experiments were done on ferritic-pearlitic steel and pearlitic steel using three different specimens, for which the effective mode II and mode III threshold values were measured and fracture surfaces were reconstructed in three dimensions using stereophotogrammetry in scanning electron microscope. The ferritic-pearlitic and pearlitic steels showed a much different behaviour of modes II and III cracks than that of the ARMCO iron. Both the deflection angle and the mode II threshold were much higher and comparable to the austenitic steel. Mechanism of shear-mode crack behaviour in the ARMCO iron, titanium and nickel were described by the model of emission of dislocations from the crack tip under a dominant mode II loading. In other tested materials the cracks propagated under a dominance of the local mode I. In the ferritic-pearlitic and pearlitic steels, the reason for such behaviour was the presence of the secondary-phase particles (cementite lamellas), unlike in the previously austenitic steel, where the fcc structure and the low stacking fault energy were the main factors. A criterion for mode I deflection from the mode II crack-tip loading, which uses values of the effective mode I and mode II thresholds, was in agreement with fractographical observations.

Physical Review Letters, 2000

The scaling laws describing the roughness development of crack surfaces are incorporated into the Griffith criterion. We show that, in the case of a Family-Vicsek scaling, the energy balance leads to a purely elastic brittle behavior. On the contrary, it appears that an anomalous scaling reflects a R-curve behavior associated to a size effect of the critical resistance to crack growth in agreement with the fracture process of heterogeneous brittle materials exhibiting a microcracking damage.