Analysis of a transiently propagating crack in functionally graded materials under mode I and II

Crack tip stress and displacement fields for a transiently propagating crack along gradient in functionally graded materials (FGMs) with a linear variation of shear modulus are developed. The higher order terms of the transient stress and displacement fields at crack tip were obtained by transforming the general partial differential equations of the dynamic equilibrium into Laplace’s equations whose solutions have harmonic functions. Thus, the fields can be expressed very simply. Using these stress components, isochromatics and the first invariant at crack tip are generated.The results show that the isochromatics (constant maximum shear stress) for mode I crack tilt backward around the crack tip with an increase of crack tip acceleration , and tilt forward around the crack tip with an increase of rate of change of dynamic mode I stress intensity factor . The isochromatics for mixed mode crack move to upper direction with an increases of and , and lower direction with an increase of . Contours of the first stress invariant for mode I crack enlarge around the crack tip with an increase of , and decrease around the crack tip with an increase of . As decreases at crack initiation, the predicted kinking angles increase. As increases, the predicted kinking angles also increase.     

A new boundary integral equation method for cracked 2-D anisotropic bodies

By using integration by parts to the traditional boundary integral formulation, a traction boundary integral equation for cracked 2-D anisotropic bodies is derived. The new traction integral equation involves only singularity of order 1/r and no hypersingular term appears. The dislocation densities on the crack surface are introduced and the relations between stress intensity factors and dislocation densities near the crack tip are induced to calculate the stress intensity factors. The boundary element method based on the new equation is established and the singular interpolation functions are introduced to model the singularity of the dislocation density (in the order of ) for crack tip elements. The proposed method can be directly used for the 2-D anisotropic body containing cracks of arbitrary geometric shapes. Several numerical examples demonstrate the validity and accuracy of BEM based on the new boundary integral equation.     

A new conservation integral for circular arc crack under multiple loads

In this paper, a path independent integral that represents the rate of energy flux at the tip during crack extension in a homogeneous and isotropic material has been derived from the principle of virtual work for a two-dimensional stationary circular arc crack subjected to multiple loads. This integral is an extension of the two-dimensional version of F-integral and includes the presence of the effects of thermal strains, initial strains and body forces, hitherto, unavailable in open literature, to the best of the authors’ knowledge. It has been further demonstrated that Rice’s J-integral, the -integral derived by Kishimoto et al. and the F-integral proposed by Lorentzon et al. are special cases of the generalized integral . The integral has been implemented into a finite element post-processing program for examining the path independence behavior under elastic and elastic-plastic deformation subjected to mechanical loads and thermo-elastic analyses under pure thermal loads. Within the limits of numerical accuracy, the application demonstrates that the solutions for the energy release rate on different contours preserve nearly identical values over the computational range.     

Ion-molecule reactions in mixtures of methane with carbon tetrafluoride

Ion-molecule reactions have been measured for methane-carbon tetrafluoride mixtures of different composition using a quadrupole mass spectrometer with a high-pressure ion source. Concentration of methane in these mixtures ranged from 10% to 90% (at 10% increment). Primary ions , , F⁺, CF⁺ and were produced by electrons with energy of 300 eV. Secondary ions , , , , and were observed as the result of ion-molecule reactions. Relative current intensities for primary and secondary ions are presented as a function of both total mixture pressure and concentration of methane in the mixture. Potential of repeller electrode inside the ion source collision chamber was fixed at 5 V for all measurements. Total mixture pressure was changed from 0.7 to 33.3 Pa. Schemes of ion-molecule reactions were proposed.     

Integral equations with hypersingular kernels--theory and applications to fracture mechanics

Hypersingular integrals of the type