An Experimental Investigation of the Size Effects in Forming Processes of High-Purity Thin Metallic Sheets


Article Preview

Miniaturization of small metallic systems can lead to a softening of the mechanical behavior due to the reduction of scale. Size effects have been considerably studied recently for materials with various crystallographic structures. Under tensile conditions, thin specimen exhibit softer mechanical properties when the number of grains across thickness is lower than a critical number and this modification appears above a critical strain level. In this work, stamping tests were performed on five hundred micrometers in thickness sheets of hexagonal closed-packed cobalt. The results are compared with those obtained for face centered cubic copper and nickel. The influence of thickness over grain size ratio was studied for several proportional loadings linked to forming processes. Complex loadings were applied with 20 mm hemispherical punch and strain paths were checked with a 3D video extensometer. Hill criterion was systematically used to take into account the anisotropy of the samples. Our results revealed that the critical strain level for which the size effects appears is strongly sensitive to the stress triaxiality which, in turn, is closely dependent to the loading path.



Main Theme:

Edited by:

C. Sommitsch, M. Ionescu, B. Mishra, E. Kozeschnik and T. Chandra




P. A. Dubos et al., "An Experimental Investigation of the Size Effects in Forming Processes of High-Purity Thin Metallic Sheets", Materials Science Forum, Vol. 879, pp. 459-464, 2017

Online since:

November 2016




* - Corresponding Author

[1] U. Engel and R. Eckstein, Microforming-from basic research to its realization, J. Mater. Process. Tec., 125-126 (2002) 35-44.

[2] M. Geiger, M. Kleiner, R. Eckstein, N. Tiesler and U. Engel, Microforming, CIRP Annals - Manufacturing Technology, 50 (2001) 445-462.


[3] A. Molotnikov, R. Lapovok, C. F. Gu, C. H. J. Davies and Y. Estrin, Size effects in micro cup drawing, Mater. Sci. Eng. A, 550 (2012) 312-319.


[4] F. Vollertsen, H. Schulze Niehoff and Z. Hu, State of the art in micro forming, Int. J. Mach. Tool. Manu., 46 (2006) 1172-1179.

[5] N. Hansen, The effect of grain size and strain on the tensile flow stress of aluminium at room temperature, Acta Metal., 25 (1977) 863-869.


[6] N. Hansen and B. Ralph, The strain and grain size dependence of the flow stress of copper, Acta Metal., 30 (1982) 411-417.

[7] C. Keller, E. Hug and X. Feaugas, Microstructural size effects on mechanical properties of high purity nickel, Int. J. Plasticity, 27 (2011) 635-654.


[8] S. Miyazaki, K. Shibata and H. Fujita, Effect of specimen thickness on mechanical properties of polycrystalline aggregates with various grain sizes, Acta Metal., 27 (1979) 855-862.


[9] T. Tabata, K. Takagi and H. Fujita, The effect on the size and deformation sub-structure on mechanical properties of polycristalline copper and Cu-Al alloys, Mat. Trans., JIM 6 (1975) 569-579.


[10] G. Fleurier, E. Hug, M. Martinez, P. A. Dubos and C. Keller, Size effects and Hall-Petch relation in polycrystalline cobalt, Phil. Mag. Let., 95 (2015) 122-130.


[11] X. Feaugas and H. Haddou, Grain-size effect on tensile behaviour of nickel and AISI 316L stainless steel, Metal. Mat. Trans., 34 A (2003) 2329-2340.


[12] E. Hug, P. A. Dubos, C. Keller, L. Duchêne and A. M. Habraken, Size effects and temperature dependence on strain-hardening mechanisms in some face centered cubic materials, Mech. Mat, 91 (2015) 136-151.


[13] E. Hug, P. A. Dubos and C. Keller, Temperature dependence and size effects on strain hardening mechanisms in copper polycrystals, Mater. Sci. Eng. A, 574 (2013) 253-261.


[14] P. A. Dubos, E. Hug, S. Thibault, M. B. Bettaieb and C. Keller, Size effects in thin face centered cubic metals for different complex forming loadings, Metal. Mat. Trans. A, 44 (2013) 5478-5487.


[15] P. A. Dubos, E. Hug, S. Thibault, A. Gueydan and C. Keller, Strain path influence on size effects during thin sheet copper microforming, Int. J. Mater. Prod. Tec., 47 (2013) 3-11.


[16] C. Keller, E. Hug, A. M. Habraken and L. Duchêne, Effect of stress path on the miniaturization size effect for nickel polycrystals, Int. J. Plasticity, 64 (2015) 26-39.


[17] Y. N. Wang and J. C. Huang, Texture analysis in hexagonal materials, Mat. Chem. Phys., 81 (2003) 11-26.

[18] Y. T. Zhu, X. Y. Zhang and Q. Liu, Observation of twins in polycrystalline cobalt containing face-center-cubic and hexagonal-close-packed phases, Mater. Sci. Eng. A, 528 (2011) 8145-8149.


[19] R. Hill, A theory of the yielding and plastic flow of anisotropy metals, Proceedings of the royal society of London, A193 (1948) 281-297.

[20] R. Hill, The mathematical theory of plasticity, ed. O. U. Press, (1950).

[21] T. A. Kals and R. Eckstein, Miniaturization in sheet metal working, J. Mater. Process. Tec., 103 (2000) 95-101.

[22] Z. Marciniak, J. L. Duncan and J. L. Hu, Mechanics of sheet metal forming, ed. Butterworth-Heinemann, (2002).