Stress-intensity factor calculations using the boundary force method

The Boundary Force Method (BFM) was formulated for the three fundamental problems of elasticity: the stress boundary value problem, the displacement boundary value problem, and the mixed boundary value problem. Because the BFM is a form of an indirect boundary element method, only the boundaries of the region of interest are modeled. The elasticity solution for the stress distribution due to concentrated forces and a moment applied at an arbitrary point in a cracked infinite plate is used as the fundamental solution. Thus, unlike other boundary element methods, here the crack face need not be modeled as part of the boundary. The formulation of the BFM is described and the accuracy of the method is established by analyzing a center-cracked specimen subjected to mixed boundary conditions and a three-hole cracked configuration subjected to traction boundary conditions. The results obtained are in good agreement with accepted numerical solutions. The method is then used to generate stress-intensity solutions for two common cracked configurations: an edge crack emanating from a semi-elliptical notch, and an edge crack emanating from a V-notch. The BFM is a versatile technique that can be used to obtain very accurate stress intensity factors for complex crack configurations subjected to stress, displacement, or mixed boundary conditions. The method requires a minimal amount of modeling effort

Boundary force method for analyzing two-dimensional cracked bodies

The Boundary Force Method (BFM) was formulated for the two-dimensional stress analysis of complex crack configurations. In this method, only the boundaries of the region of interest are modeled. The boundaries are divided into a finite number of straight-line segments, and at the center of each segment, concentrated forces and a moment are applied. This set of unknown forces and moments is calculated to satisfy the prescribed boundary conditions of the problem. The elasticity solution for the stress distribution due to concentrated forces and a moment applied at an arbitrary point in a cracked infinite plate are used as the fundamental solution. Thus, the crack need not be modeled as part of the boundary. The formulation of the BFM is described and the accuracy of the method is established by analyzing several crack configurations for which accepted stress-intensity factor solutions are known. The crack configurations investigated include mode I and mixed mode (mode I and II) problems. The results obtained are, in general, within + or - 0.5 percent of accurate numerical solutions. The versatility of the method is demonstrated through the analysis of complex crack configurations for which limited or no solutions are known

A re-evaluation of finite-element models and stress-intensity factors for surface cracks emanating from stress concentrations

A re-evaluation of the 3-D finite-element models and methods used to analyze surface crack at stress concentrations is presented. Previous finite-element models used by Raju and Newman for surface and corner cracks at holes were shown to have ill-shaped elements at the intersection of the hole and crack boundaries. These ill-shaped elements tended to make the model too stiff and, hence, gave lower stress-intensity factors near the hole-crack intersection than models without these elements. Improved models, without these ill-shaped elements, were developed for a surface crack at a circular hole and at a semi-circular edge notch. Stress-intensity factors were calculated by both the nodal-force and virtual-crack-closure methods. Both methods and different models gave essentially the same results. Comparisons made between the previously developed stress-intensity factor equations and the results from the improved models agreed well except for configurations with large notch-radii-to-plate-thickness ratios. Stress-intensity factors for a semi-elliptical surface crack located at the center of a semi-circular edge notch in a plate subjected to remote tensile loadings were calculated using the improved models. The ratio of crack depth to crack length ranged form 0.4 to 2; the ratio of crack depth to plate thickness ranged from 0.2 to 0.8; and the ratio of notch radius to the plate thickness ranged from 1 to 3. The models had about 15,000 degrees-of-freedom. Stress-intensity factors were calculated by using the nodal-force method

Thermalization in a quasi-1D ultracold bosonic gas

We study the collisional processes that can lead to thermalization in one-dimensional systems. For two body collisions excitations of transverse modes are the prerequisite for energy exchange and thermalzation. At very low temperatures excitations of transverse modes are exponentially suppressed, thermalization by two body collisions stops and the system should become integrable. In quantum mechanics virtual excitations of higher radial modes are possible. These virtually excited radial modes give rise to effective three-body velocity-changing collisions which lead to thermalization. We show that these three-body elastic interactions are suppressed by pairwise quantum correlations when approaching the strongly correlated regime. If the relative momentum $k$ is small compared to the two-body coupling constant $c$ the three-particle scattering state is suppressed by a factor of $(k/c)^{12}$, which is proportional to $\gamma ^{12}$, that is to the square of the three-body correlation function at zero distance in the limit of the Lieb-Liniger parameter $\gamma \gg 1$. This demonstrates that in one dimensional quantum systems it is not the freeze-out of two body collisions but the strong quantum correlations which ensures absence of thermalization on experimentally relevant time scales.Comment: revtex4, 3 figures. Final version of the text, accepted for publication (see journal ref.

Exciton energy transfer in nanotube bundles

Photoluminescence is commonly used to identify the electronic structure of individual nanotubes. But, nanotubes naturally occur in bundles. Thus, we investigate photoluminescence of nanotube bundles. We show that their complex spectra are simply explained by exciton energy transfer between adjacent tubes, whereby excitation of large gap tubes induces emission from smaller gap ones via Forster interaction between excitons. The consequent relaxation rate is faster than non-radiative recombination, leading to enhanced photoluminescence of acceptor tubes. This fingerprints bundles with different compositions and opens opportunities to optimize them for opto-electronics.Comment: 5 pages, 5 figure