Mixed mode axisymmetric annular cracks in a finite layer: Off angle crack initiation

The solutions of axisymmetric Volterra type climb and glide edge dislocations are obtained in a layer by means of the Hankel transforms. Utilizing the same procedure, Green’s function solution is obtained for a layer under self-equilibration normal ring traction. The distributed dislocation technique is used to construct integral equations for a system of co-axial annular cracks where the layer is under axisymmetric normal loads. These equations are solved numerically to obtain dislocation density on the cracks surfaces. The results are employed to determine stress intensity factors for annular and penny-shaped cracks and the interaction between two co-axial penny-shaped cracks is studied. Moreover, the stress intensity factors of the interacting cracks are determined such that they can be further used in conjunction with strain energy density (SED) failure criterion to obtain the possible direction of crack initiation that may not be apparent under mixed mode conditions.     

On isometries of euclidean planes

Journal of Geometry - In [1,5 ] the authors prove that any transformation of the euclidean plane,coordinatized by the real field, which preserves a single non-zero distance is necessarily an...     

Theoretical study of hybrid TEA–CO2 lasers

Temporal and spatial analysis of dynamics of hybrid transversely excited atmospheric pressure (TEA)–CO₂ lasers is studied using two different models with four and eight energy levels. These models are used for simulation of the laser and computing the output energy. Effects of several parameters such as input energies and gas mixture concentrations (especially presence of CO molecules) are also studied.     

On the phase field modeling of crack growth and analytical treatment on the parameters

Continuum Mechanics and Thermodynamics - A thermodynamically consistent phase field model for crack propagation is analyzed. The thermodynamic driving force for the crack propagation is derived...     

The Intra-cavity Mode Competition and Laser Absorption Spectroscopy with CO2 Laser

A mathematical model is developed for analysis the dynamics of an intra-cavity laser spectroscopy and mode competition using the CO₂ laser as the coherent source. The governing equations of system are derived and effect of the absorbing material on the laser modes, as a time-dependent term is considered. Thus, the application of the CO₂ laser for intra-cavity laser spectroscopy with considering an inhomogeneous medium and effect of the absorbing material is investigated.     

A characterization of isometries of rational Euclidean spaces

We show that an injection of the rational Euclidean n-space, n5, which preserves the distances e, 1/2e, e an arbitrary non-zero rational number, is necessarily an isometry. Further, we show that the above characterization fails in case n=3 or 4.     

Semi-exact solution for thermo-mechanical analysis of functionally graded elastic-strain hardening rotating disks

In this paper, distributions of stress and strain components of rotating disks with non-uniform thickness and material properties subjected to thermo-elasto-plastic loading are obtained by semi-exact method of Liao’s homotopy analysis method (HAM) and finite element method (FEM). The materials are assumed to be elastic-linear strain hardening and isotropic. The analysis of rotating disk is based on Von Mises’ yield criterion. A two dimensional plane stress analysis is used. The distribution of temperature is assumed to have power forms with the hotter point located at the outer surface of the disk. A mathematical technique of transformation has been proposed to solve the homotopy equations which are originally hard to be handled. The domain of the solution has been substituted by a new domain through which the unknown variable has been taken out from the argument of the function. This makes the solution much easier. A numerical solution of the governing differential equations is also presented based on the Runge–Kutta’s method. The results of three methods are presented and compared which shows good agreements. This verifies the implementation of the HAM and demonstrates its applicability to provide accurate solution for a very complicated case of strongly high nonlinear differential equations with no exact solution. It is important to notice that compared with other methods, HAM needs significant more computation time and computer hardware requirements which limit its application for those problems that other methods can easily handle them.     

Effects of stress invariants and reverse loading on ductile fracture initiation

Recent research studies on ductile fracture of metals have shown that the ductile fracture initiation is significantly affected by the stress state. In this study, the effects of the stress invariants as well as the effect of the reverse loading on ductile fracture are considered. To estimate the reduction of load carrying capacity and ductile fracture initiation, a scalar damage expression is proposed. This scalar damage is a function of the accumulated plastic strain, the first stress invariant and the Lode angle. To incorporate the effect of the reverse loading, the accumulated plastic strain is divided into the tension and compression components and each component has a different weight coefficient. For evaluating the plastic deformation until fracture initiation, the proposed damage function is coupled with the cyclic plasticity model which is affected by all of the stress invariants and pervious plastic deformation history.For verification and evaluation of this damage-plasticity constitutive equation a series of experimental tests are conducted on high-strength steel, DIN 1.6959. In addition finite element simulations are carried out including the integration of the constitutive equations using the modified return mapping algorithm. The modeling results show good agreement with experimental results.     

On distance preserving transformations of Euclidean-like planes over the rational field

Aequationes mathematicae -