Jean-Paul Jernot

Mechanical Properties of Flax Fibers and of the Derived Unidirectional Composites

Flax fibers were used to process unidirectional composites by two different methods. Their mechanical properties obtained by tensile testing are discussed with respect to the properties of the fibers and those of the matrix (unsatured polyester). The similarity of the tensile curves of the composites and of the elementary fibers is attributed to the good adhesion of the fibers with the matrix. Moreover, as there is almost a linear evolution of the composite properties with the fiber volume fraction, these properties are used to estimate those of the real reinforcement material, that is, the flax bundles: the calculations lead to a fiber strength of 500-800 MPa and a fiber modulus of roughly 30 GPa, which is half the values obtained by tensile testing elementary fibers. These data may be helpful when trying to model the deformation behavior of flax fiber-reinforced composites.

Morphological analysis of sintering

In this paper mathematical morphology is applied to describe the microstructural changes of metal powders during sintering. We show which morphological parameters are accessible to rapid and automatic methods. Of these parameters the change in the connectivity number and the concavity number enable the various stages of sintering to be distinguished. Moreover the growth of the necks between powder particles can be followed using a morphological method of analysis to reveal them. This method can be applied to the investigation of the microstructure of any material consisting of convex grains.

Three-dimensional simulation of flow through a porous medium

A three‐dimensional simulated random packing of spheres is digitized and progressively densified with dilations of the initial stacking. Flow of fluid through these successive structures is then simulated with geodesic dilations inside the porous phase. The results allow a clear distinction to be made between two factors affecting the flow: the metric properties and the topological properties of the porous network.

Topological description of the densification of a granular medium

The densification of a granular medium is described in terms of topological parameters. Two successive cases are quantitatively analysed starting from regular three‐dimensional (3‐D) packings (in continuous and digitized space) and simulated random 3‐D packings of monosized spheres.

Euler‐Poincaré characteristic of a randomly filled three‐dimensional network

The random filling of a three‐dimensional face‐centred cubic network is simulated on a computer at increasing densities between 0 and 1. The Euler‐Poincaré characteristic (for the spaces ℝ0, ℝ1, ℝ2 and ℝ3) is then measured on all the simulated structures. A quantitative description of this simple densification process is obtained and the maxima observed correspond to the highest values practically attainable for the stereological parameters.

Local contributions to the Euler–Poincaré characteristic of a set

The Euler–Poincaré characteristic (EPC) of a polyconvex subset X of Rd can be evaluated by covering the subset with an auxiliary tessellation, measuring its contribution within each cell of the tessellation and adding all contributions. Two different ways are proposed to define the contribution of a cell to the EPC of X. These contributions turn out to be related by duality formulae. Finally, three applications are given: the measurement of the EPC on adjacent fields, the measurement of the EPC on discretized images and the detection of defects in atomic structures.

Evolution of gaussian curvature in a simulated densifying structure

Unfortunately, these 3-D topological parameters are not accessible from a 2-D analysis. Moreover, morphological transformations and automatic image analysis can be performed only if the structure is digitized in 3-D space. For the 3-D digitization of the structure, a grid in which the points form the dense face centered cubic (FCC) network of crystallography was chosen (Bhanu Prasad et al., 1988). A point with its twelve neighbours at the same distance can be taken as a unit structuring element allowing the basic transformations of mathematical morphology on the 3-D digitized structure. The EPC of the 3-D sets is calculated using Euler’s relation (Bhanu Prasad et a1.,1988) and the shell correction method (Bhanu Prasad et a1.,1989) for local analysis. Balls of same radii stacked in a FCC structure digitized and dilated in 3-D space were used as a test. A very good agreement was found between the measured values of NV and the theoretical calculations (Bhanu Prasad & Jernot) (Bhanu Prasad & Jernot, 1990). Then, a first application of this 3-D analysis is the simulation of a densifying process. For this purpose, a simulated random packing of monosized spheres (Visscher & Bolsterli, 1972) was digitized. on the 3-D FCC grid. The densification of this packing has been made with two transformations of the mathematical morphology : dilation and closing. These successive 3-D transformations of the packing increase its volumic fraction, Vv(S1, and the topological evolution of the structure can be monitored, for each step, with the determination of the Gaussian curvature (figures). At the very beginning of the process, the slight decrease of GV is attributed to a densification without major topological changes. Then, an abrupt increase is observed corresponding to the coalescence of the spheres and isolation of cavities. At the end, the elimination of these cavities leads to GV = 0. The main difference between the two densification processes is that the dilation emphasizes the

Young’s Modulus of Plant Fibers

A simple model is used to explain the decrease of the Young’s modulus of plant fibers as the apparent diameter is increased. The assumption made in this work is that the fiber consists of a very thin but stiff outer shell, and a thicker but less stiff inner shell which defines the load bearing area. The model is favorably compared with the experimental data reported in the literature for flax, hemp and stinging nettle fibers.