Asymmetric LSCF Membranes Utilizing Commercial Powders

Powders of constant morphology and quality are indispensable for reproducible ceramic manufacturing. In this study, commercially available powders were characterized regarding their microstructural properties and screened for a reproducible membrane manufacturing process, which was done by sequential tape casting. Basing on this, the slurry composition and ratio of ingredients were systematically varied in order to obtain flat, crack-free green tapes suitable for upscaling of the manufacturing process. Debinding and sintering parameters were adjusted to obtain defect-free membranes with diminished bending. The crucial parameters are the heating ramp, sintering temperature, and dwell time. The microstructure of the asymmetric membranes was investigated, leading to a support porosity of approximately 35% and a membrane layer thickness of around 20 µm. Microstructure and oxygen flux are comparable to asymmetric La0.6Sr0.4Co0.2Fe0.8O3−δ (LSCF) membranes manufactured from custom-made powder, showing an oxygen flux of > 1 mL⋅cm−2⋅min at 900 °C in air/Ar gradient.

Role of the Cu substrate in the growth of ultra-flat crack-free highly-crystalline single-layer graphene

Producing ultra-flat crack-free single-layer high-quality graphene over large areas has remained the key challenge to fully exploit graphene's potential into next-generation technological applications.

Oore-Burns Function of Form Application in Numerical Treatment of Mode I Flat Crack Problem in Infinite Body

The general approach of numerical treatment of integro-differential equation of the flat crack problem is considered. It consists in presenting the crack surface loading as the set of the polynomial functions of two Cartesian coordinates while the corresponding crack surface displacements are chosen as the similar polynomials multiplied by the function of form (FoF) which reflects the required singularity of their behavior. To find the relations matrixes between these two sets a new effective numerical procedure for the integration over the area of arbitrary shape crack is developed. In based on the classical hyper-singular method, i.e. Laplace operator is initially analytically applied to the integral part of equation and the resulting hyper singular equation is subsequently considered. The presented approach can be implemented with any variant of FoF, but Oore-Burns FoF, which was earlier suggested in their famous 3D weight function method, is supposed to be the most accurate and universal. It takes into account all points of crack contour, which provides perfect physical conditionality of the solution, but such FoF is relatively heavy in implementation and of low computational speed. The special procedure is developed for the approximation of the crack contour of arbitrary shape by the circular and straight segments. It allows to easily obtain analytical expression for Oore-Burns FoF, which greatly increases the calculation speed and accuracy. The accuracy of the considered method is confirmed by the examples of the circular, elliptic, semicircular and square cracks at different polynomial laws of loading. The developed methods are used in the implemented procedure for crack growth simulation. It allows to model growth of crack of arbitrary shape at arbitrary polynomial loading, at that all contour points are taken into account and can expand with their own speeds each. Procedure has high accuracy and don’t need complex and high-cost re-meshing process between the iterations unlike FEM or other numerical methods. At that usage of Oore-Burns FoF provides high flexibility of the presented approach: unlike similar theoretical methods, where FoF calculation procedure is rigidly connected with the crack shape, which complicates the adequate crack growth modeling, the used FoF automatically takes into account all points of crack contour, even if its shape became complex during the growth. Presented crack growth procedure can be effectively used to test accuracy and correctness of correspondent numerical methods, including the newest XFEM approach.

Two-Dimensional Elastodynamic Scattering by a Finite Flat Crack

The diffraction of elastic harmonic waves by a finite plane tunnel crack is studied. A solution is derived from an analysis of the integral equations describing the problem, using the Wiener–Hopf technique and the method of compound asymptotic expansions. Taking into account the successive reflections of Rayleigh waves from crack tips, an approximate analytical solution is expressed in a closed-form that is computationally effective and yields accurate results in the resonance region of dimensionless wave numbers. Both direct and inverse scattering problems are considered.

Semianalytical Method for the SIF Calculation for a Crack of Arbitrary Shape in Infinite Body

The exact analytical approach for stress intensity factor calculation for an arbitrary shape mode I crack loaded by the polynomial stresses is proposed. The approach is based on the calculation of the crack faces displacement at given loading. The displacement field is presented as a shape function multiplied by an adjustment polynomial. At that the key problem is the solution of well-known inverse task: obtaining the stresses field at the crack faces on the base of a given displacements field. Multiply solution of such task for a whole set of certain displacements base functions (e.g., for the single terms of the adjustment polynomial) allows to get analytical expression which connects stresses and displacements fields. The original semi-analytical technique for integration with subsequent differentiation of well-known singular integral equation of the flat crack problem is developed. The excellent accuracy of the method is confirmed for an elliptic crack as well as for a rectangular one in the infinite 3D body. New results are given for an inner semi-elliptic crack in the infinite body which surfaces are loaded by polynomial stresses up to the 6th order. The importance of choosing the appropriate shape function is demonstrated.