INVESTIGATION OF LÜDERS DEFORMATION IN THE MILD STEEL

The features of macroscopic strain inhomogeneity in the form of Chernov–Lüders bands development on elastic-plastic transition were investigated in the mild steel. The main regularities of nucleation and propagation of the bands are established. Particular attention was paid to the kinetics of moving boundaries (fronts) of bands, characteristic velocities were determined. It is shown that the rate of formation of nucleus of the Chernov–Lüders band is more than an order of magnitude higher than the rate of its expansion. Situations are considered when more than one band develops simultaneously in the object and therefore several moving fronts are observed. It is established that in all cases the velocities of fronts of the Chernov–Lüders bands are mutually consistent so that at any instant the generalized rate of expansion of the deformed zone is a constant value. The effect of the deformation rate on the kinetics of the Chernov–Lüders fronts was analyzed. Both the generalized rate of expansion of the deformed zone and the speed of individual fronts increase with the increase of the loading rate. A  nonlinear (power-law) character of this dependence is established. The fronts of the bands have a complex structure. Different parts of the front can move with unequal velocities, so that the front line is locally curved and split. Ahead of the front, in the undeformed part of the sample, the forerunners may appear, the configuration of which resembles the Chernov–Lüders bands nuclei. When encountering the fronts of adjacent bands are annihilated. Annihilation of the fronts is a complex process, which is also characterized by the formation of a precursor and secondary diffusion Chernov–Lüders bands. These facts demonstrate that a simplified view of the Chernov-Lüders band as a deformed region in a loaded sample, and the front of the band as a boundary between deformed and undeformed zones, should be revised. The microscopic theory of Lüders deformation is based on the avalanche growth of the density of mobile dislocations due to breaking from an obstacles and subsequent multiplication, which is realized simultaneously at the upper yield point within the crystallite (grain). At the same time, to form a mobile macroscopic deformation front it is necessary that plastic deformation should be transferred to neighboring grains without hardening, that is, grain-boundary accommodation is needed. The results obtained in the paper suggest that such a zone of accommodation is apparently the Chernov–Lüders band front, and, therefore, it has a complex structure.

mild steel, elastic-plastic transition, instability of plastic flow, Chernov–Lüders bands

1. Pelleg J. Mechanical properties of materials. Heidelberg, New York, London: Springer, 2013, 633 p.

2. Physical metallurgy. Vol. 3. Cahn R.W., Haasen P. eds. Amsterdam: North-Holland Pub. Company, 1983, 630 p.

3. Honeycombe R.W.K. The plastic deformation of metals. New York: Edw. Arnold Publ., 1968, 402 p.

4. Chrysochoos A., Louche H. An infrared image processing to analyses the calorific effects accompanying strain localization. International Journal of Engineering Science. 2000, vol. 38, no. 16, pp.  1759–1788.

5. Sun H.B., Yoshida F., Ohmori M., Ma X. Effect of strain rate on Lüders band propagating velocity and Lüders strain for annealed mild steel under uniaxial tension. Materials Letters. 2003, vol. 57, no. 29, pp. 4535–4539.

6. Avril S., Pierron F., Sutton b M. A., Yan J. Identification of elastovisco-plastic parameters and characterization of Lüders behavior using digital image correlation and the virtual fields method. Mechanics of Materials. 2008, vol. 40, no. 9, pp. 729–742.

7. Plekhov O.A., Naimark O.B., Saintier N., Palin-Luc T. Elasticplastic transition in iron: Structural and thermodynamic features. Technical Physics. 2009, vol. 54, no. 8, pp. 1141–1146.

8. Cottrell A.H. Dislocation and plastic flow in crystals. Oxford: Clarendon press, 1953. (Russ.ed.: Cottrell A.H. Dislokatsii i plasticheskoe techenie v kristallakh. Moscow: Metallurgizdat, 1958, 267 p.).

9. Conrad H. Effect of stress on the Lüders band velocity in low carbon steels. Journal of the Mechanics and Physics of Solids. 1963, vol.  11, pp. 437–440.

10. Johnston W.G., Gilman J.J. Dislocation velocities, dislocation densities, and plastic flow in lithium fluoride crystals. J. Appl. Phys. 1959, vol. 30, pp. 129–134.

11. Dudarev E.F. Mikroplasticheskaya deformatsiya i predel tekuchesti polikristallov [Microplastic deformation and yield stress of polycrystals]. Tomsk: izd. TGU, 1988, 256 p. (In Russ.).

12. Zuev L.B., Gorbatenko V.V., Pavlichev K.V. Elaboration of speckle photography techniques for plastic flow analyses. Measur. Sci. Technol. 2010, vol. 21, no. 5, pp. 054014–054019.

13. Jones R., Wykes C. Holographic and Speckle Interferometry. Cambridge, London, New York: Cambridge Univ. Press, 1983, 328 p.

14. Cottrell A.H., Bilby B.A. Dislocation theory of yielding and strain ageing in iron. Proceedings of Physics Society. 1949, vol. A62, pp.  49–62.

15. Gorbatenko V.V., Danilov V.I., Zuev L.B. Elastoplastic transition in material with sharp yield point. AIP Conf. Proc. 2015, vol. 1683, pp. 020058.

16. Gorbatenko V.V., Danilov V.I., Zuev L.B. Plastic flow instability: Chernov–Lüders bands and the Portevin–Le Chatelier effect. Technical Physics. 2017, vol. 62, no. 3, pp. 395–400.

17. Hahn G.T. A model for yielding with special reference to the yieldpoint phenomena of iron and related bcc metals. Acta Metall. 1962, vol. 10, pp. 727–738.

18. Žerovnik A., Pepel V., Prebil I., Kunc R. The yield-point phenomenon and cyclic plasticity of the uniaxially loaded specimens. Materials and Design. 2016, vol. 92, pp. 971–977.

19. Beardsmore D.W., Quinta da Fonseca J., Romero J., English C.A., Ortner S.R., Sharples J., Sherry A.H., Wilkes M.A. Study of Lüders phenomena in reactor pressure vessel steels. Materials Science & Engineering. 2013, vol. A588, pp. 151–166.

20. Armstrong R.W., Zerilli F.J. Dislocation mechanisms aspects of plastic instability and shear banding. Mech. Mater. 1994, vol. 17, no. 1, pp. 319–327.