Theoretical study of the generation of screw dislocations for Rayleigh and Lamb waves in isotropic solids

Phase singularities are generic structures which occur in all wave fields, and they are characterised by an inability to assign a value to the phase. Screw dislocations are a particular kind of phase singularity where the phase possesses a helical structure, with the singularity at the centre of the helix. In this paper we show that it is possible to generate screw dislocations on the surface of elastic isotropic solids by means of the interference of three Rayleigh waves or three Lamb waves. The dispersive character of Lamb waves leads to more complicated behaviour, which may in turn result in greater potential for applications.     

双螺杆转子的受力分析

从双螺杆转子螺旋曲面的参数方程出发，利用空间解析几何理论将转子三维螺旋面坐标映象为对应不同压力腔的二维积分区域，在整个积分区域积分可以计算作用在双螺杆压缩机，双螺杆泵螺旋面转子上的力和力矩。本文以一种双螺杆泵的转子为例，利用本方法进行了受力分析，解析出转子受力，力矩随转子转角的变化关系。     

Closed-form solution for a mode-III interfacial edge crack between two bonded dissimilar elastic strips

A closed-form solution is obtained for the problem of a mode-III interfacial edge crack between two bonded semi-infinite dissimilar elastic strips. A general out-of-plane displacement potential for the crack interacting with a screw dislocation or a line force is constructed using conformal mapping technique and existing dislocation solutions. Based on this displacement potential, the stress intensity factor (SIF, K_III) and the energy release rate (ERR, G_III) for the interfacial edge crack are obtained explicitly. It is shown that, in the limiting special cases, the obtained results coincide with the results available in the literature. The present solution can be used as the Green’s function to analyze interfacial edge cracks subjected to arbitrary anti-plane loadings. As an example, a formula is derived correcting the beam theory used in evaluation of SIF (K_III) and ERR (G_III) of bimaterials in the double cantilever beam (DCB) test configuration.     

Multiple moving cracks in a functionally graded strip

This paper considers several finite moving cracks in a functionally graded material subjected to anti-plane deformation. The distributed dislocation technique is used to carry out stress analysis in a functionally graded strip containing moving cracks under anti-plane loading. The Galilean transformation is employed to express the wave equations in terms of coordinates that are attached to the moving crack. By utilizing the Fourier sine transformation technique the stress fields are obtained for a functionally graded strip containing a screw dislocation. The stress components reveal the familiar Cauchy singularity at the location of dislocation. The solution is employed to derive integral equations for a strip weakened by several moving cracks. Numerical examples are provided to show the effects of material properties, the crack length and the speed of the crack propagating upon the stress intensity factor.     

New phenomena concerning a screw dislocation interacting with two imperfect interfaces

Dislocation mobility and stability in nanocrystals and electronic materials are influenced by the material composition and interface conditions. Its mobility and stability then affect the mechanical behaviors of the composites. In this paper, we first address, in detail, the problem of a screw dislocation located in an annular coating layer which is imperfectly bonded to the inner circular inhomogeneity and to the outer unbounded matrix. Both the inhomogeneity-coating interface and coating-matrix interface are modeled by a linear spring with vanishing thickness to account for the possible damage occurring on the interface. An analytic solution in series form is derived by means of complex variable method, with all the unknown constants being determined explicitly. The solution is then applied to the study of the dislocation mobility and stability due to its interaction with the two imperfect interfaces. The most interesting finding is that when the middle coating layer is more compliant than both the inner inhomogeneity and the outer unbounded matrix and when the interface rigidity parameters for the two imperfect interfaces are greater than certain values, one stable and two unstable equilibrium positions can exist for the dislocation. Furthermore, under certain conditions an equilibrium position, which can be either stable or unstable (i.e., a saddle point), can exist, which has never been observed in previous studies. Results for a screw dislocation interacting with two parallel straight imperfect interfaces are also presented as the limiting case where the radius of the inner inhomogeneity approaches infinity while the thickness of the coating layer is fixed.     

Computational fluid dynamics simulation and redesign of a screw conveyor reactor

National Renewable Energy Laboratory (NREL) designed a shrinking-bed reactor to maintain a constant bulk packing density of cellulosic biomass. The high solid-to-liquid ratio in the pretreatment process allows a high sugar yield and avoids the need to flush large volumes of solution through the reactor. To scale up the shrinking-bed reactor, NREL investigated a pilot-scale screw conveyor reactor in which an interrupted flight between screws was employed to mimic the “shrinking-bed” effect. In the experiments with the screw conveyor reactor, overmixing and uneven flow occurred. These phenomena produce negative effects on biomass hydrolysis. The flow behavior inside the reactor was analyzed to allow redesign of the screw to achieve adequate mixing and even flow. In the present study, computational fluid dynamics (CFD) was utilized to simulate the fluid flow in the porous media, and a new screw design was proposed. CFD analysis performed on the redesigned reactor indicated that an even flow pattern was achieved.     

Anti-plane analysis of an orthotropic strip weakened by several moving cracks

In this paper several finite cracks with constant length (Yoffe-type crack) propagating in an orthotropic strip were studied. The distributed dislocation technique is used to carry out stress analysis in an orthotropic strip containing moving cracks under anti-plane loading. The solution of a moving screw dislocation is obtained in an orthotropic strip by means of Fourier transform method. The stress components reveal the familiar Cauchy singularity at the location of dislocation. The solution is employed to derive integral equations for a strip weakened by moving cracks. Finally several examples are solved and the numerical results for the stress intensity factor are obtained. The influences of the geometric parameters, the thickness of the orthotropic strip, the crack size and speed have significant effects on the stress intensity factors of crack tips which are displayed graphically.     

Low-density polycarbonate composites with robust hollow glass microspheres by tailorable processing variables

Polycarbonate (PC) composites with low weight have been required for mobile applications. Herein, the incorporation of 15 phr (parts per hundred of resin) soda-lime borosilicate hollow glass microspheres (HGMs) into a PC matrix reduced the specific gravity by 15.2%. The microsphere preservation rate was systematically examined depending on HGM compressive strength, and processing conditions for extrusion (side-feeding vs. main-feeding vs. screw configuration) and injection molding (mild condition for edge gate vs. extreme condition for pinpoint gate). Various transition temperatures such as glass transition temperatures and heat distortion temperature were investigated as a function of HGM. The coefficient of thermal expansion of the 15 phr HGM-embedded PC composites was reduced by 51.9%. The rheological behavior of the composites was also probed. The toughness was reduced due to the ductile-to-brittle transition of PC caused by the incorporation of fillers despite the enhanced modulus. The incorporation of the robust hollow glass microspheres into a PC composite via a delicately designed screw configuration and suitable processing conditions can be used for low-density composites such as mobile applications.     

On the screw dislocation in a functionally graded material

This paper presents the stress field of a screw dislocation in a medium graded in y-direction. The medium is exponentially graded. For such a graded material theories of elasticity as well as gradient elasticity are applied. By means of the stress function technique we found exact analytical solutions of the corresponding master equations. Using the stress field, the Peach–Koehler force is given. The axial symmetry of a screw dislocation is lost due to the gradation in the y-direction.