Fracture of disordered solids in compression as a critical phenomenon: III. Analysis of the localization transition

The properties of the Hamiltonian developed in Paper II are studied showing that at a particular strain level a ``localization'' phase transition occurs characterized by the emergence of conjugate bands of coherently oriented cracks. The functional integration that yields the partition function is then performed analytically using an approximation that employs only a subset of states in the functional neighborhood surrounding the most probable states. Such integration establishes the free energy of the system, and upon taking the derivatives of the free energy, the localization transition is shown to be continuous and to be distinct from peak stress. When the bulk modulus of the grain material is large, localization always occurs in the softening regime following peak stress, while for sufficiently small bulk moduli and at sufficiently low confining pressure, the localization occurs in the hardening regime prior to peak stress. In the approach to localization, the stress-strain relation for the whole rock remains analytic, as is observed both in experimental data and in simpler models. The correlation function of the crack fields is also obtained. It has a correlation length characterizing the aspect ratio of the crack clusters that diverges as (\xi \sim (\ep_{c}-\ep)^{-2}) at localization.Comment: 11 pages, 3 figure

X-ray photoelectron emission microscopy in combination with x-ray magnetic circular dichroism investigation of size effects on field-induced N\'eel-cap reversal

X-ray photoelectron emission microscopy in combination with x-ray magnetic circular dichroism is used to investigate the influence of an applied magnetic field on N\'eel caps (i.e., surface terminations of asymmetric Bloch walls). Self-assembled micron-sized Fe(110) dots displaying a moderate distribution of size and aspect ratios serve as model objects. Investigations of remanent states after application of an applied field along the direction of N\'eel-cap magnetization give clear evidence for the magnetization reversal of the N\'eel caps around 120 mT, with a $\pm$20 mT dispersion. No clear correlation could be found between the value of the reversal field and geometrical features of the dots

Chemical Switching Behaviour of Tricarbonylrhenium(I) Complexes of a New Redox Active ‘Pincer’ Ligand

The structures and optoelectronic properties of tricarbonylrhenium(I) complexes of di(2-pyrazolyl-p-tolyl)amine in its neutral and deprotonated (uninegative amido) form were investigated. Reactions of the complexes with Brønsted acids or bases result in distinctive changes of colour and electrochemical activity owing to the non-innocent nature of the ligand

Using Sterics to Promote Reactivity in \u3cem\u3efac\u3c/em\u3e-Re(CO)\u3csub\u3e3\u3c/sub\u3e Complexes of Some ‘Non-Innocent’ NNN-Pincer Ligands

Two new redox active ligands based on di(2-(3-organopyrazolyl)-p-tolyl)amine have been prepared in order to investigate potential effects of steric bulk on the structures, electronic properties, or reactivity of tricarbonylrhenium(I) complexes. Replacing the hydrogens at the 3-pyrazolyl positions with alkyl groups causes significant distortion to the ligand framework due to potential interactions between these groups when bound to a fac-Re(CO)3 moiety. The distortions effectively increase the nucleophilic character of the central amino nitrogen and ligand-centered reactivity of the metal complexes

A General Criterion for Liquefaction in Granular Layers with Heterogeneous Pore Pressure

International audienceFluid-saturated granular and porous layers can undergo liquefaction and lose their shear resistance when subjected to shear forcing. In geosystems, such a process can lead to severe natural hazards of soil liquefaction, accelerating slope failure, and large earthquakes. Terzaghi's principle of effective stress predicts that liquefaction occurs when the pore pressure within the layer becomes equal to the applied normal stress on the layer. However, under dynamic loading and when the internal permeability is relatively small the pore pressure is spatially heterogeneous and it is not clear what measurement of pore pressure should be used in Terzaghi's principle. Here, we show theoretically and demonstrate using numerical simulations a general criterion for liquefaction that applies also for the cases in which the pore pressure is spatially heterogeneous. The general criterion demands that the average pore pressure along a continuous surface within the fluid-saturated granular or porous layer is equal to the applied normal stress

Downscaling of fracture energy during brittle creep experiments

We present mode 1 brittle creep fracture experiments along fracture surfaces that contain strength heterogeneities. Our observations provide a link between smooth macroscopic time-dependent failure and intermittent microscopic stress-dependent processes. We find the large-scale response of slow-propagating subcritical cracks to be well described by an Arrhenius law that relates the fracture speed to the energy release rate. At the microscopic scale, high-resolution optical imaging of the transparent material used (PMMA) allows detailed description of the fracture front. This reveals a local competition between subcritical and critical propagation (pseudo stick-slip front advances) independently of loading rates. Moreover, we show that the local geometry of the crack front is self-affine and the local crack front velocity is power law distributed. We estimate the local fracture energy distribution by combining high-resolution measurements of the crack front geometry and an elastic line fracture model. We show that the average local fracture energy is significantly larger than the value derived from a macroscopic energy balance. This suggests that homogenization of the fracture energy is not straightforward and should be taken cautiously. Finally, we discuss the implications of our results in the context of fault mechanics