C.P. Jiang

Edge dislocation interacting with an interfacial crack along a circular inhomogeneity

Abstract The elastic interaction of an edge dislocation, which is located either outside or inside a circular inhomogeneity, with an interfacial crack is dealt with. Using Riemann–Schwarz’s symmetry principle integrated with the analysis of singularity of the complex potentials, the closed form solutions for the elastic fields in the matrix and inhomogeneity regions are derived explicitly. The image force on the dislocation is then determined by using the Peach–Keohler formula. The influence of the crack geometry and material mismatch on the dislocation force is evaluated and discussed when the dislocation is located in the matrix. It is shown that the interfacial crack has significant effect on the equilibrium position of the edge dislocation near a circular interface. The results also reveal a strong dependency of the dislocation force on the mismatch of the shear moduli and Poisson’s ratios between the matrix and inhomogeneity.

A screw dislocation interacting with an interphase layer between a circular inhomogeneity and the matrix

The interaction of a screw dislocation with an interphase layer between a circular inhomogeneity and the matrix is dealt with. By combining the sectionally holomorphic function, Cauchy integral and Laurent series expansion techniques, the relation among the complex potentials for the three material regions is given, and the functional equation in complex potential for the interphase layer are derived. Explicit series solutions are given for the two cases when the screw dislocation is located in the inhomogeneity or in the matrix. The influence of the interphase layer parameters on interaction energy and dislocation force is evaluated and discussed. The present solutions contain a number of novel and previously known results which can be shown to be special cases.

Antiplane problems of collinear rigid line inclusions in dissimilar media

Abstract Antiplane problems of two dissimilar materials with rigid line inclusions along their common straight interface are dealt with. A method is proposed for solving such problems by the application of the Riemann-Schwarz symmetry principle which is integrated with the analysis of singularity of complex functions. The formulation of the general problem and the closed form solutions for some of the problems of practical importance are presented. The stress distribution in the immediate vicinity of the rigid line end is examined, and a comparison is made with that near the crack lip. The formulation and solutions for corresponding homogeneous materials are only special cases when the shear moduli of the two media are the same, and as a consequence some classical formulation and results can again be rederived.

A universal Biot number determining the susceptibility of ceramics to quenching

A universal Biot number of ceramics, which not only determines the susceptibility of the ceramics to quenching but also indicates the duration that the ceramics fail during thermal shock, is theoretically obtained. The present analysis shows that the thermal shock failure of the ceramics with a Biot number greater than this universal value is a very rapid process that just occurs in the initial regime of the heat conduction of the ceramics. This universal Biot number provides a guide to the selection of the ceramics applying to the thermostructural engineering including thermal shock.

Universal Biot number determining stress duration and susceptibility of ceramic cylinders to quenching

A universal Biot number, which not only describes the susceptibility of ceramic cylinders to quenching but also determines the duration that ceramic cylinders are subjected to thermal stress during thermal shock, is theoretically obtained. The analysis proves that thermal shock failure of ceramic cylinders with a Biot number greater than the critical value is a rapid process, which only occurs in the initial heat conduction regime. The results provide a guide to the selection of ceramic materials for thermostructural engineering, with particular reference to thermal shock.

Prediction of effective stagnant thermal conductivities of porous materials at high temperature by the generalized self-consistent method

The generalized self-consistent method is developed to deal with porous materials at high temperature, accounting for thermal radiation. An exact closed form formula of the local effective thermal conductivity is obtained by solving Laplaces equation, and a good approximate formula with uncoupled conductive and radiative effects is given. A comparison with available experimental data and theoretical predictions demonstrates the accuracy and efficiency of the present formula. Numerical examples provide a better understanding of interesting interaction phenomena of pores in heat transfer. It is found that the local effective thermal conductivity divides into two parts. One, attributed to conduction, is independent of pore radius for a fixed porosity and, furthermore, is independent of temperature (actually, it is approximately independent of the temperature) if it is non-dimensionalized by the thermal conductivity of the matrix. The other is due to thermal radiation in pores and strongly depends on the temperature and pore radius. The radiation effect can not be neglected at high temperature and in the case of relatively large pores.

A four-phase confocal elliptical cylinder model for predicting the effective thermal conductivity of coated fibre composites

A four-phase confocal elliptical cylinder model is proposed from which a generalised self-consistent method is developed for predicting the thermal conductivity of coated fibre reinforced composites. The method can account for the influence of the fibre section shape ratio on conductivity, and the physical reasonableness of the model is demonstrated by using the fibre distribution function. An exact solution is obtained for thermal conductivity by applying conformal mapping and Laurent series expansion techniques of the analytic function. The solution to the three-phase confocal elliptical model, which simulates composites with idealised fibre–matrix interfaces, is arrived at as the degenerated case. A comparison with other available micromechanics methods, Hashin and Shtrikmans bounds and experimental data shows that the present method provides convergent and reasonable results for a full range of variations in fibre section shapes and for a complete spectrum of the fibre volume fraction. Numerical results show the dependence of the effective conductivities of composites on the aspect ratio of coated fibres and demonstrate that a coating is effective in enhancing the thermal transport property of a composite. The present solutions are helpful to analysis and design of composites.