Elastic Moduli Of Inclusion Research Articles

The concentration parameter thermal microstresses as the thermophysical characteristics of two-phase materials

Thermal strength is one of the main thermophysical characteristics of structural materials. For homogeneous systems it is determined by the strength characteristics of the material. While for inhomogeneous systems, in particular, multiphase ones, it is necessary to consider the nature of the microstructure. Heat resistant real materials such as steels are known to be multi-phase systems. One of the mechanisms of their destruction is associated with the presence of propagating heat fluxes that generate thermal stresses. The aim of this paper is to evaluate the patterns of the formation of spatial distributions of thermal stresses in matrix systems of round inclusions characterized by different mutual disposition. The spatial distributions of thermal stresses in a two-phase material characterized by a matrix structure with round inclusions are investigated. For the numerical solution of the problem of stationary thermal conductivity the finite element method with discretization of the medium by triangular elements is used. It was found that at certain points in the medium the values of thermal stresses are ten times higher than the average for the material. It is shown that the spatial distribution and the local magnitude of the temperature gradient depend on the shape of the particles of the phase components and the values of their thermal conductivities. It is considered that the elastic moduli of inclusion and matrix differ little from each other.

Micromechanics of randomly oriented ellipsoidal inclusion composites. Part II: Elastic moduli

The elastic moduli of composites containing randomly oriented ellipsoidal inclusions are derived, calculated from the average stress and the average strain in the matrix and the inclusions, obtained using a modified Eshelby model. The quantitative expressions for the elastic moduli of the composite are obtained in relation to the volume fraction, the shape, and the elastic moduli of the inclusions. Specific cases are discussed: First, the elastic moduli of the materials containing randomly oriented penny-shaped microcracks are derived and compared with those obtained by Budiansky and O’Connell [Int. J. Solids Struct. 12, 81 (1976)] and Nemat-Nasser and Hori. The general expressions for the elastic moduli of multiphase inclusion composites and the effect of porosity or in the form of isolated voids on the elastic moduli of homogeneous materials and inclusion containing composites are derived. Experimental results have been employed to compare the predictions with engineering materials.

Separation at a circular interface under biaxial load

T his p aper is concerned with the plane problem of the decohesion of a smooth circular elastic inclusion from an unbounded elastic matrix subject to a remote biaxial load. The phenomenon of brittle decohesion is treated as a problem of bifurcation of equilibrium separation at the inclusion-matrix interface. In accordance with other cohesive zone type models the interface is characterized by a constitutive equation relating tractions across the interface to the displacement discontinuity that develops there. The specific form considered in this work is the physically based nonlinear force law of Ferrante, Smith and Rose that couples the normal component of displacement jump to the normal component of interface traction and which requires a characteristic length for its prescription. Under decreasing values of characteristic length to inclusion radius ratio, three types of separation behavior (ductile decohesion, brittle decohesion, closure) can occur provided the remote load, interface strength and elastic moduli of inclusion and matrix are within the required bounds. Within this context of interfacial separation, the phenomenon of void nucleation is briefly examined and a connection is made between the classical nucleation criteria of critical interfacial stress and critical energy release and the criteria for ductile and brittle decohesion. Interaction effects are analysed in an approximate way by considering the effects of decohesion on a hypothetical, rigidly bonded inclusion with the same elastic moduli as the matrix.

Photo-elastic analysis of shrinkage micro cracking in concrete

Synopsis The paper deals with the stress distribution in concrete during the variations in volume due to hydration of the cement paste at early ages. A two-dimensional model was devised for the photo-elastic study of the stress distribution. The model consisted of a square array of circular inclusions made of pure epoxy polymer embedded in a matrix made of plasticized epoxy resin. Shrinkage stresses developed during the curing of the matrix around the already hardened inclusions. The elastic moduli of inclusions and matrix were chosen so that their ratio approximated to the ratio of the elastic moduli of aggregate and the hardened cement paste in concrete. Although this model is a simplified, plane configuration of the three-dimensional random arrangement of the aggregate in concrete, it depicts fairly accurately the state of stress around aggregate particles. Tensile stresses, developing at the interface between aggregate and cement paste, cause the development of micro crocks at the interface during the curing period of concrete and before any application of load. The effect of the ratio of the average diameter of aggregates to the average clear distance between them upon the stress distribution was also studied.