This study presents a new theoretical determination of yield stress for pure mono-crystal materials based on the concept of the Efficient Area of Stress (EAS). From the atomic yield stress on the atomic surface a², given by the model of Orowan, the macroscopic yield stress is then obtained through a Scale Law of Measure (SLM) which depends only on the lattice spacing and a constant L. This relation shows that the efficient atomic dimension is a fractal dimension. The precision obtained by the SLM is of an atomic order compared to the error (102 to 104 MPa) obtained by classical theories. The SLM gives also new theoretical relations for the elastic limit of strain, the toughness and the fracture strength. The SLM is finally extended to non pure materials to take into account the microstructures (grain size, impurity, phases, solutions, etc.) and the temperature effects by introducing the concept of an "efficient atomic distance".


Yield stress ; atomic cleavage fracture ; scale factor ; efficient area of stress ; fractal

Texte intégral :

PDF (English)


- Kelly A., Tyson W.R., Cottrell A.H., Phil. Mag., 15, (1967), p.567.

- Macmillan N.H., J. Mat. Sci., 7, (1972), p. 239.

- Dorlot J.M. , Baillon J.P., Massounave J., "Des Matériaux", Ed. Ecole Tech. Montréal.

- Orowan E., (1984), Cleavage Fracture of metals, Rep. Prog. Phy., 12, (1986), p. 185.

- Ashby M.F. , Jones D.R.H., "Matériaux", Dunod, (1991).

- O Hall E., Proc. Phys. Soc., 64B, (1951), p. 163.

- Petch N.J., J. of Iron Steel, 173, (1953), p. 25.

- Stroh A.N., Proc. R. Soc., A222, (1954), p. 404.

- Cottrel A.H., Trans. Ame. Inst. Min. Metall. Petrol. Engrs., 212, (1958), p. 192.

- Smith E., "Proc. Conf. Phys. Basis of yield and Fract", Phys. Soc., Oxford, (1966).

- Murakami S., "Notion of Continuum Damage Mechanics and its Application to Anisotropic Creep Damage Theory", J. Eng. Mat. and Technology, 105, (1983), p. 99.

- Hult J., "Continuum Damage Mechanics – Capabilities, imitations and Promises, Mechanisms of Deformation and Fracture", Pergamon Oxford, (1979), p. 233.

- Chaboche J.L., "Continuum Damage Mechanics; Part I- General Concepts", Journal of Applied Mechanics, 55, (1988), pp. 59-64.

- Crajcinovic D., "Continuum damage Mechanics", Applied Mechanics Review, 37, (1984), p. 1.

- Pluvinage G., "Exercices de Mécanique élasto-plastique", Cépaduès-Edition, (1997).

- Chaudron G., "Monographie sur les matériaux de haute pureté", Masson, (1977).

- Hume-Rothery W., "Elements of structural metallurgy", The Institute of Metals London, Monograph and Report Series, n°26, (1961).

- Raynor G.V., "The theory of alloy phases", ASM, Metal Park, OH, (1956), p. 321.

- Axon H.J. and Hume-Rothery W., Proc. Of Roy. Soc., A 193, (1948), p. 1.

- Massalsky T.B. and King H.W., Proc. Mat. Sci., 10, (1961), p. 1.

- Eshelby J.D., Solid State Physic, 3, (1956), 79.

- Vergard L., Z. Crystal., 67, (1928), p. 239.

- Friedel J., Phil. Mag., 46, (1955), p. 514.

- Guttman L., Solid State Physics, 3, (1956), p. 145.

- Bragg W.L. and Williams E.J, Proc. Roy. Soc., London, A145, (1934), p. 669.

- Beth H.A., Proc. Roy. Soc., London, A150, (1935), p. 552.

- Pearson W.B., "A handbook of lattice spacing and structures of metals & alloys", Pergamon Press, London, & New York, (vol. 1, 1958 and vol. 2, 1967).

- Mitra G.B. and Mitra S.K., Indian J. of Physics., 37, (1963), p. 462.

- Schmitz B., Pranghe N. and Dunner P., Z. Metallkd, 59, (1968), p. 377.

- Medoff J.I. and Cadoff I., J. of Metals, 11, (1959), p. 581.

- Wassilewsky R.J., Trans. Met. Soc. AIME, 221, (1961), p. 1231.

- Christ B. and Smith G.V., Act. Met., 15, (1967), p. 809.


  • Il n'y a présentement aucun renvoi.


Direction des Publications et de l'animation scientifique

Université des Frères Mentouri Constantine 1. Route Ain El-Bey. 25000. Algérie.