Computation of brittle fracture propagation in strain gradient materials by the FEniCS library

Strain gradient continuum damage modelling has been applied to quasistatic brittle fracture within an approach based on a maximum energy-release rate principle. The model was implemented numerically, making use of the FEniCS open-source library. The considered model introduces non-locality by taking into account the strain gradient in the deformation energy. This allows for stable computations of crack propagation in differently notched samples. The model can take wedges into account, so that fracture onset can occur at wedges. Owing to the absence of a damage gradient term in the dissipated energy, the normal part of the damage gradient is not constrained on boundaries. Thus, non-orthogonal and non-parallel intersections between cracks and boundaries can be observed.

Fault dip variations related to elastic layering

Summary In this paper we model the crack growth in an elastic medium constituted by two welded half-spaces with different rigidities. We implement a 2D Boundary Element Method (BEM) computing shear and normal tractions acting on the crack and the slip accommodating stress drop from an arbitrary initial configuration to a final frictional configuration. The direction of crack growth follows the criterion of maximum energy release (strain and gravitational energy) provided that it overcomes the surface fracture energy and the work dissipated by friction. The energetic criterion leads to estimates of the dip angle of seismic faults depending on the amplitude of the initial stress and it includes the classical Anderson's results as a particular case. Moreover, in presence of a sharp rigidity contrast, the direction of crack growth is strongly deflected. The model simulates non-planar, complex, fault geometries, as in the case of detachment and listric faults and it explains the increase of dip angles for both normal and reverse faults, when they enter soft sedimentary layers.

Энерговыделение при бомбардировке атомами дейтерия поверхности вольфрама

The distribution of energy release (linear energy loss) over depth was calculated when bombarded with deuterium atoms of a tungsten target in a wide energy range of incident particles of 100 eV - 10 MeV. It is shown that in the energy range up to 100 keV, the maximum energy release, contrary to the prevailing ideas, is near the surface of a solid. At energies above 100 keV, the nature of the distribution changes and the Bragg maximum appears near the point where the particle stops. The distribution of the energy release over depth in tungsten is obtained for conditions typical of the ITER tokamak reactor, which makes it possible to estimate the wall heating during bombardment by plasma atoms.

Crack Tunneling in Cement Sheath of Hydrocarbon Well

In a hydrocarbon well, cement fills the annular gap between two steel casings or between a steel casing and rock formation, forming a sheath that isolates fluids in different zones of the well. For a well as long as several kilometers, the cement sheath covers a large area and inevitably contains small cracks. The cement sheath fails when a small crack grows and tunnels through the length of the well. We calculate the energy release rate at a steady-state tunneling front as a function of the width of the tunnel. So long as the maximum energy release rate is below the fracture energy of the cement, tunnels of any width will not form. This failsafe condition requires no measurement of small cracks, but depends on material properties and loading conditions. We further show that the critical load for tunneling reduces significantly if the cement/casing and cement/formation interfaces slide.

SIMULATION OF CRACK PROPAGATION IN TWO DIMENSIONAL PROBLEMS

Predicting crack trajectory when crack propagation occurs plays an important role in fracture mechanics problems because this will evaluate whether important areas of structure are heavily influenced by crack propagation. This article will introduce three theories to predict crack path, including maximum tangential stress theory, maximum energy release rate theory and minimum strain energy density theory. Besides, the FRANC2D program is used to simulate the crack propagation based on three above theories.

Modeling of Dislocations and Mismatched Layers in Pentagonal Nanorods

Pentagonal nanorods (PNRs) are crystalline objects with unique fivefold symmetry. They are often experimentally observed for materials with FCC crystal structure. In an ideal case a PNR consists of five elastically distorted but otherwise perfect crystalline regions divided by low-energy twin boundaries. The elastic distortions in PNRs and associated stored elastic energy are effectively described in the framework of a disclination approach. As a result of mechanical stress relaxation, the stored energy can be diminished in expense of structural defect formation in PRN interior. It is demonstrated that a perfect multiple twinned PNR structure is unstable with respect to dislocation formation, i.e. prismatic dislocation loop or straight edge dislocation, for PNRs above a certain critical diameter. A new mechanism for the relaxation processes in PNRs is theoretically investigated. This mechanism assumes the formation of the shell possessing crystal lattice mismatch with respect to the PNR core region. The optimal magnitude for core/shell crystal lattice mismatch and optimal shell thickness providing maximum energy release for this mechanism of mechanical stress relaxation, are predicted.

Propagation and Deflection of Electric-Field-Induced Microcracks in 0.69Pb(Mg1/3Nb2/3)O3-0.31PbTiO3 Ferroelectric Single Crystals

Propagation and deflection of microcracks driven by electric loading in <001>-oriented 0.69Pb(Mg1/3Nb2/3)O3-0.31PbTiO3 ferroelectric single crystals were investigated using an in-situ transmission electron microcopy (TEM) technique. The static observation of the domain pattern revealed the coexistence of sub-micrometer and nano-meter domains. Electric field induced deviation from the main microcrack path and subsequent propagation along the direction almost perpendicular to the electric field were observed directly. A qualitative analyses is given based on the maximum energy release rate criterion.