Nickel; Size effects; Hall-Petch; FE simulation; Stress path; Temperature
Abstract :
[en] The critical dimension (e.g. thickness for sheet, diameter for cylindrical part) of small components used in a miniaturized system is often a crucial factor affecting the mechanical behavior and the forming process, since in such length scale ranges the grain size is comparative to the mechanical part dimension. To have a better understanding of the mechanical behavior of microsized metallic parts, the size effects in 500 µm thick samples of nickel sheet were studied in tensile and shear loading states. The modifications of the mechanical behavior due to different numbers of grains across the thickness were thoroughly investigated at room temperature and 573 K. New experimental results obtained by shear tests at high temperature revealed that the transition from polycrystalline to multicrystalline behavior is more pronounced in tensile loading than in shearing conditions and that different surface sample state is observed. It was demonstrated that the reduced stress level effect depends not only on the temperature, but also on the stress state. In addition, with a moderate increase in temperature, the surface effects leading to the multicrystalline behaviors became more predominant in tensile condition than in shearing condition.
Engel, U., Eckstein, R., Microforming—from basic research to its realization. J. Mater. Process. Technol. 125–126 (2002), 35–44, 10.1016/S0924-0136(02)00415-6.
Cui, Z., Leach, R., Lewis, A., Singleton, L., Standardisation for microsystems technology : the way forward. Proceedings of the 8th International Conference on the Commercialization of Micro and Nano Systems: COMS 2003, 8-11 September 2003, Amsterdam, 2003, COMS.
Hwang, J.K., Effects of diameter and preparation of round shaped tensile specimen on mechanical properties. Mater. Sci. Eng. A, 763, 2019, 138119, 10.1016/j.msea.2019.138119.
Fu, M.W., Chan, W.L., A review on the state-of-the-art microforming technologies. Int. J. Adv. Manuf. Technol. 67 (2013), 2411–2437, 10.1007/s00170-012-4661-7.
Fu, M.W., Chan, W.L., Micro-scaled Products Development via Microforming-Deformation Behaviours, Processes, Tooling and its Realization. 2014, Springer-Verlag London, 10.1007/978-1-4471-6326-8.
Geiger, M., Kleiner, M., Eckstein, R., Tiesler, N., Engel, U., Microforming. CIRP Ann. - Manuf. Technol. 50 (2001), 445–462, 10.1016/S0007-8506(07)62991-6.
Espinosa, H.D., Prorok, B.C., Peng, B., Plasticity size effects in free-standing submicron polycrystalline FCC films subjected to pure tension. J. Mech. Phys. Solid. 52 (2004), 667–689, 10.1016/j.jmps.2003.07.001.
Greer, J.R., De Hosson, J.T.M., Plasticity in small-sized metallic systems: intrinsic versus extrinsic size effect. Prog. Mater. Sci. 56 (2011), 654–724, 10.1016/j.pmatsci.2011.01.005.
Nix, W.D., Gao, H., Indentation size effects in crystalline materials: a law for strain gradient plasticity. J. Mech. Phys. Solid. 46 (1998), 411–425, 10.1016/S0022-5096(97)00086-0.
Dong, H., Wen, B., Melnik, R., Relative importance of grain boundaries and size effects in thermal conductivity of nanocrystalline materials. Sci. Rep., 4, 2014, 7037, 10.1038/srep07037.
Mohri, K., Uchiyama, T., Shen, L.P., Cai, C.M., Panina, L.V., Sensitive micro magnetic sensor family utilizing magneto-impedance (MI) and stress-impedance (SI) effects for intelligent measurements and controls. Sensors Actuators, A Phys. 91 (2001), 85–90, 10.1016/S0924-4247(01)00620-3.
Janssen, P.J.M., Hoefnagels, J.P.M., de Keijser, T.H., Geers, M.G.D., Processing induced size effects in plastic yielding upon miniaturisation. J. Mech. Phys. Solid. 56 (2008), 2687–2706, 10.1016/j.jmps.2008.03.008.
Yang, B., Motz, C., Rester, M., Dehm, G., Yield stress influenced by the ratio of wire diameter to grain size - a competition between the effects of specimen microstructure and dimension in micro-sized polycrystalline copper wires. Philos. Mag. A 92 (2012), 3243–3256, 10.1080/14786435.2012.693215.
Verheyden, S., Pires Da Veiga, L., Deillon, L., Mortensen, A., The effect of size on the plastic deformation of annealed cast aluminium microwires. Scripta Mater. 161 (2019), 58–61, 10.1016/j.scriptamat.2018.10.009.
Shin, C., Lim, S., Jin, H.H., Hosemann, P., Kwon, J., Specimen size effects on the weakening of a bulk metastable austenitic alloy. Mater. Sci. Eng. A 622 (2015), 67–75, 10.1016/j.msea.2014.11.004.
Dai, C.Y., Zhang, B., Xu, J., Zhang, G.P., On size effects on fatigue properties of metal foils at micrometer scales. Mater. Sci. Eng. A 575 (2013), 217–222, 10.1016/j.msea.2013.03.064.
Fu, M.W., Yang, B., Chan, W.L., Experimental and simulation studies of micro blanking and deep drawing compound process using copper sheet. J. Mater. Process. Technol. 213 (2013), 101–110, 10.1016/j.jmatprotec.2012.08.007.
Fu, H.H., Benson, D.J., Meyers, M.A., Analytical and computational description of effect of grain size on yield stress of metals. Acta Mater. 49 (2001), 2567–2582, 10.1016/S1359-6454(01)00062-3.
Janssen, P.J.M., de Keijser, T.H., Geers, M.G.D., An experimental assessment of grain size effects in the uniaxial straining of thin Al sheet with a few grains across the thickness. Mater. Sci. Eng. A 419 (2006), 238–248, 10.1016/J.MSEA.2005.12.029.
Klein, M., Hadrboletz, A., Weiss, B., Khatibi, G., The ‘size effect’ on the stress-strain, fatigue and fracture properties of thin metallic foils. Mater. Sci. Eng. A 319–321 (2001), 924–928, 10.1016/S0921-5093(01)01043-7.
Miyazaki, S., Shibata, K., Fujita, H., Effect of specimen thickness on mechanical properties of polycrystalline aggregates with various grain sizes. Acta Metall. 27 (1979), 855–862, 10.1016/0001-6160(79)90120-2.
Simons, G., Weippert, C., Dual, J., Villain, J., Size effects in tensile testing of thin cold rolled and annealed Cu foils. Mater. Sci. Eng. A 416 (2006), 290–299, 10.1016/j.msea.2005.10.060.
Geißdörfer, S., Engel, U., Geiger, M., FE-simulation of microforming processes applying a mesoscopic model. Int. J. Mach. Tool Manufact. 46 (2006), 1222–1226, 10.1016/j.ijmachtools.2006.01.019.
Hug, E., Dubos, P.A., Keller, C., Duchêne, L., Habraken, A.M., Size effects and temperature dependence on strain-hardening mechanisms in some face centered cubic materials. Mech. Mater. 91 (2015), 136–151, 10.1016/j.mechmat.2015.07.001.
Keller, C., Hug, E., Feaugas, X., Microstructural size effects on mechanical properties of high purity nickel. Int. J. Plast. 27 (2011), 635–654, 10.1016/j.ijplas.2010.08.002.
Fourie, J.T., The flow stress gradient between the surface and centre of deformed copper single crystals. Philos. Mag. A J. Theor. Exp. Appl. Phys. 17 (1968), 735–756, 10.1080/14786436808223026.
Chan, W.L., Fu, M.W., Lu, J., Liu, J.G., Modeling of grain size effect on micro deformation behavior in micro-forming of pure copper. Mater. Sci. Eng. A 527 (2010), 6638–6648, 10.1016/j.msea.2010.07.009.
Fu, S., Yu, D., Chen, Y., An, K., Chen, X., Size effect in stainless steel thin wires under tension. Mater. Sci. Eng. A, 2020, 139686, 10.1016/j.msea.2020.139686.
Xu, Z.T., Peng, L.F., Fu, M.W., Lai, X.M., Size effect affected formability of sheet metals in micro/meso scale plastic deformation: experiment and modeling. Int. J. Plast. 68 (2015), 34–54, 10.1016/j.ijplas.2014.11.002.
Zheng, J.Y., Yang, H.P., Fu, M.W., Ng, C., Study on size effect affected progressive microforming of conical flanged parts directly using sheet metals. J. Mater. Process. Technol. 272 (2019), 72–86, 10.1016/j.jmatprotec.2019.05.007.
Diehl, A., Engel, U., Geiger, M., Influence of microstructure on the mechanical properties and the forming behaviour of very thin metal foils. Int. J. Adv. Manuf. Technol. 47 (2010), 53–61, 10.1007/s00170-008-1851-4.
Molotnikov, A., Lapovok, R., Gu, C.F., Davies, C.H.J., Estrin, Y., Size effects in micro cup drawing. Mater. Sci. Eng. A 550 (2012), 312–319, 10.1016/j.msea.2012.04.079.
Vollertsen, F., Hu, Z., Niehoff, H.S., Theiler, C., State of the art in micro forming and investigations into micro deep drawing. J. Mater. Process. Technol. 151 (2004), 70–79, 10.1016/j.jmatprotec.2004.04.266.
Dubos, P.A., Hug, E., Thibault, S., Ben Bettaieb, M., Keller, C., Size effects in thin face-centered cubic metals for different complex forming loadings. Metall. Mater. Trans. A Phys. Metall. Mater. Sci. 44 (2013), 5478–5487, 10.1007/s11661-013-1892-7.
Whiteley, R.L., The importance of directionality in drawing quality sheet steel. Trans. ASM 52 (1960), 154–162.
Michel, J.F., Picart, P., Size effects on the constitutive behaviour for brass in sheet metal forming. J. Mater. Process. Technol. 141 (2003), 439–446, 10.1016/S0924-0136(03)00570-3.
Saotome, Y., Yasuda, K., Kaga, H., Microdeep drawability of very thin sheet steels. J. Mater. Process. Technol. 113 (2001), 641–647, 10.1016/S0924-0136(01)00626-4.
Keller, C., Hug, E., Habraken, A.M., Duchêne, L., Effect of stress path on the miniaturization size effect for nickel polycrystals. Int. J. Plast. 64 (2015), 26–39, 10.1016/j.ijplas.2014.07.001.
Eichenhueller, B., Egerer, E., Engel, U., Microforming at elevated temperature - forming and material behaviour. Int. J. Adv. Manuf. Technol. 33 (2007), 119–124, 10.1007/s00170-006-0731-z.
Hug, E., Dubos, P.A., Keller, C., Temperature dependence and size effects on strain hardening mechanisms in copper polycrystals. Mater. Sci. Eng. A 574 (2013), 253–261, 10.1016/j.msea.2013.03.025.
Peirs, J., Verleysen, P., Paepegem, W Van, Degrieck, J., Determining the stress-strain behaviour at large strains from high strain rate tensile and shear experiments. Int. J. Impact Eng. 38 (2011), 406–415, 10.1016/j.ijimpeng.2011.01.004.
Keller, C., Hug, E., Chateigner, D., On the origin of the stress decrease for nickel polycrystals with few grains across the thickness. Mater. Sci. Eng. A 500 (2009), 207–215, 10.1016/j.msea.2008.09.054.
Evers, L.P., Parks, D.M., Brekelmans, W.A.M., Geers, M.G.D., Crystal plasticity model with enhanced hardening by geometrically necessary dislocation accumulation. J. Mech. Phys. Solid. 50 (2002), 2403–2424, 10.1016/S0022-5096(02)00032-7.
Levenberg, K., Arsenal, F., A method for the solution of certain non-linear problems in least squares. Q. Appl. Math. 1 (1943), 536–538.
Marquardt, D.W., An algorithm for least-squares estimation of nonlinear parameters. J. Soc. Ind. Appl. Math. 11 (1963), 431–441, 10.1137/0111030.
Zhu, Y.Y., Cescotto, S., Unified and mixed formulation of the 8-node hexahedral elements by assumed strain method. Comput. Methods Appl. Mech. Eng. 129 (1996), 177–209, 10.1016/0045-7825(95)00835-7.
Hall, E.O., The deformation and ageing of mild steel: II Characteristics of the Lüders deformation. Proc. Phys. Soc. B 64 (1951), 742–747, 10.1088/0370-1301/64/9/302.
Petch, N.J., The cleavage strength of polycrystals. J. Iron Steel Inst. Inst. 174 (1953), 25–28.
Armstrong, R.W., 60 years of hall-petch: past to present nano-scale connections. Mater. Trans. 55 (2014), 2–12, 10.2320/matertrans.MA201302.
Xu, J., Zhu, X., Shan, D., Guo, B., Langdon, T.G., Effect of grain size and specimen dimensions on micro-forming of high purity aluminum. Mater. Sci. Eng. A 646 (2015), 207–217, 10.1016/j.msea.2015.08.060.
Cai, W., Nix, W.D., Imperfections in Crystalline Solids. 2016, Cambridge University Press, 10.1017/CBO9781316389508.
