Showing papers on "Representative elementary volume published in 1989"

Capillary fingering: percolation and fractal dimension

Abstract: We present experimental and theoretical results concerning immiscible displacements (drainage) in 2-dimensional permeable media. When capillary forces are predominant, the injected fluid presents very thin fingers and the ‘Representative Elementary Volume’ concept cannot be used for describing the partial saturations. The purpose of this paper is to show how this classical concept can be replaced by a statistical approach based on ‘fractal’ geometry.

The effect of interfacial conditions on the elastic-longitudinal modulus of fibre reinforced composites

Abstract: A model study is conducted on the prediction of the elastic longitudinal modulusE CL of a unidirectional fibre reinforced composite. It is assumed in our model that the fibres are aligned in the uniaxial loading direction and that the representative volume element (RVE) consists of three coaxial cylinders, namely the fibre, the interphase and the bulk matrix. The interphase represents the third phase developed between the constituent phases of the composite and it is characterized by mechanical imperfections, physicochemical interactions and limited mobility of macromolecules due to their absorption on the filler surface. Thus the interphase properties are varied within this third phase in an unknown way. In the present study it is supposed that the elastic modulus of the interphase materialE i is varied along the thickness following an exponential law of variation. Moreover, the interphase thickness is determined according to existing theory which is based on thermal capacity measurements. PredictedE CL values agree well with respective experimental results. In addition the effect of an abrupt variation of the elastic modulus at the fibre surface onE CL is considered. Results showed that this type of variation is of minor importance in predictingE CL.

The Effect of Weak Interface on Transverse Properties of a Ceramic Matrix Composite

Abstract: Experimental studies conducted at the NASA Lewis Research Center on silicon carbide reaction-bonded silicon nitride composite system (SiC/RBSN) led to a significant observation regarding their unidirectional tensile properties. It was found that transverse stiffness and strength were much lower than those predicted from existing analytical models based on good interfacial bonding. Since the composite system was designed to have weakened interfaces to improve toughness, it was believed that these weakened interfaces were responsible for the decrease in transverse properties. To support this claim, a two dimensional finite element analysis was performed for a transverse representative volume element. Specifically, the effect of fiber/matrix displacement compatibility at the interface was studied under both tensile and compressive transverse loadings. Interface debonding was represented active gap elements connecting the fiber and matrix. The analyses show that the transverse tensile strength and stiffness are best predicted when a debonded interface is assumed for the composite. In fact, the measured properties can be predicted by simply replacing the fibers by voids. Thus, the following two conclusions are drawn from the present study: (1) little or no interfacial bonding exists in the SiC/RBSN composite; (2) an elastic analysis can predict the transverse stiffness and strength.

Continuum Modeling of the Development of Intralaminar Cracking in Composite Laminates

Abstract: Intralaminar cracking in composite laminates has been found to develop as a set of parallel cracks whose average spacing reduces with increasing stress level or with increasing number of cycles of a given stress amplitude. The average crack spacing has been found in some instances to approach a minimum which has been interpreted as saturation or characteristic state. These features of the intralaminar cracking are predicted by the continuum model presented here. The model characterizes the intralaminar cracking by a second–order damage tensor defined on a representative volume element of the cracked laminate and describes the development of this cracking by the rate of the damage tensor. The components of the damage rate tensor are treated as response functions subjected to the initial material symmetry restrictions. An incremental solution to the rate equations shows that the crack density is an exponential function of the strain and displays the experimentally observed characteristics.