Theory of irradiation hardening of metals and alloys based on the energy condition of plasticity
UDC: 539.214 + 621.039.531
A conventional approach for estimating the yield strength consists in calculation of a critical shear stress for bowing out of gliding dislocation segments between barriers. According to Orovan theory, the critical shear stress τk is determined by the average distance l between obstacles: τk = αGb / l, where α is the constant; G is the shear module; b is the Burgers vector.The superposition of various barriers is taken into account as additive of different contributions τk = τ1 + τ2 + τ3 + …, or as τk2= τ12+ τ22+ τ32+ … . Both procedures have yet no theoretical ground. On the basis of the maximum shear stress concept, the critical shear stress τk in polycrystals is related to the tensile yield strength σy as follows: σy = 2τk (Tresca criterion). On the basis of the effective stress concept this relationship has well known form: σy = (√3)τk (Mises criterion). Sometimes the Taylor criterion is used, according to which σy = 3.06τk. In the present paper an another method of calculating the yield strength of metals and alloys is proposed. The energy condition of plasticity (Mises criterion) is used. According to this condition the plastic flow of a material occurs when the deformation potential energy which is proportional to the square of the effective stress σeff , reaches a certain limiting value proportional to the square of the yield stress σy under uniaxial tension.
In this paper, it is assumed that for the onset of plastic flow the specific potential energy of deformation caused by external forces should exceed the limiting value equal to the potential energy of deformation created by all microstructure defects (dislocations, dislocation loops, voids, precipitates, etc.). Such an approach allows to calculate barrier strengthening coefficients α. Also, according to this approach the total yield stress is equal to the square root of the sum of yield stress squares for different types of crystal defects («geometric superposition of strengthening barriers contributions»).
- Orowan E., in: Internal Stresses in Metals and Alloys. Institute of Metals, London, 1948, p. 451.
- Diehl J. and Seidel G.P. Proc. Symp. on Radiation Damage in Reactor Materials, IAEA, Vienna, 1969, v. 1, p.187.
- Bement A.L. Jr. in: Strength of Metals and Alloys. Proceedings of Second International Conference, ASM International. Metals Park, OH, 1973, p. 693.
- Was G.S. Fundamentals of Radiation Materials Science: Metals and Alloys, SpringerVerlag, New York, 2007, 827 p.
- Garner F.A., Hamilton M.L., Panayotou N.F., Johnson G.D. The microstructural origins of yield strength changes in AISI 316 during fission or fusion irradiation. J. Nucl. Mater. 1981, v. 103104, pp. 803808.
- Kuleshova E.A., Gurovich B.A., Shtrombakh Ya.I., Nikolaev Yu.A., Pechenkin V.A. Microstructural behavior of VVER440 reactor pressure vessel steels under irradiation to neutron fluences beyond the design operation period. J. Nucl. Mater., 2005, v. 342, pp. 7789.
- Hill R. The Mathematical Theory of Plasticity, Oxford, Clarendon Press, 1950.
- Friedel J. Dislocations. Pergamon Press, 1964.
- Landau L.D. and Lifshitz E.M. Theory of Elasticity. Moscow. Nauka Publ., 1965 (in Russian).
- Ashby M.F. and Brown L.M. Diffraction Contrast from Spherically Symmetrical Coherency Strains. Phil. Mag. 1963, v. 8 , no. 91, p. 1083.
- Buswell J.T., Phythian W.J., МсElroy R.J., Dumbill S., Ray P.H.N., Mace J. and Sinclair R.N. Irradiationinduced microstructural changes, and hardening mechanisms, in model PWR reactor pressure vessel steels. J. Nucl. Mater. 1995, v. 225, p. 196.
- Odette G.R. and Lucas G.E. Radiation Embrittlement of Nuclear Reactor Pressure Vessel Steels: An International Review, ASTM STP 909, Volume 2. The American Society for Testing and Materials, 1986, p. 206.
- Fisher S.B. and Buswell J.T. A Model For PWR PressureVessel Embrittlement. Int. J. Press. Vessel & Piping. 1987, v. 27, no. 2, pp. 91135.
- Williams T.J., Burch P.R., English C.A. and Ray P.H.N. Proc. 3rd Int. Symp. on Environmental Degradation of Materials in Nuclear Power Systems – Water Reactors, Traverse City, MI, USA (The Metallurgical Society), 1988, p. 121.
- Keating D.T. and Goland A.N. Atomic Displacements around Dislocation Loops. J. Appl. Physics, 1968, v. 39, no. 13, p. 6018.
- Tucker R.P., Ohr S.M. and Wechsler M.S. Proc. Symp. on Radiation Damage in Reactor Materials, IAEA, Vienna, 1969, v. 1, p. 215.
- Moteff J., Michel D.J. and Sikka M.L. in: Defects and Defects Clusters in BCC Metals and Their Alloys. Ed. by Arsenault R.J. Nuclear Metallurgy, 1973, v. 18, p. 198.