First-order size effects in the mechanic of miniaturized
components
Citation for published version (APA):
Hoefnagels, J. P. M., Janssen, P. J. M., Keijser, de, T. H., & Geers, M. G. D. (2008). First-order size effects in the mechanic of miniaturized components. In B. A. Schrefler, & U. Terego (Eds.), Proceedings of the 8th World Congress on Computational Mechanics, Italy, Venice (pp. CD-rom-)
Document status and date: Published: 01/01/2008 Document Version:
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8th. World Congress on Computational Mechanics (WCCM8) 5th European Congress on Computational Methods in Applied Sciences and Engineeering (ECCOMAS 2008) June 30 –July 5, 2008 Venice, Italy
FIRST-ORDER SIZE EFFECTS IN THE MECHANICS OF
MINIATURISED COMPONENTS
P.J.M. Janssen1, J.P.M. Hoefnagels2, Th.H. de Keijser1, M.G.D. Geers2 1 The Netherlands Institute
for Metals Research (NIMR) P.O.Box 5008, 2600GA, Delft, The Netherlands
2 Eindhoven University of
Technology,Mech. Eng. Dep.
P.O.Box 513, 5600MB,
Eindhoven, The Netherlands j.p.m.hoefnagels@tue.nl
Key Words: Miniaturization, size effects, microstructure, experimental-numerical analysis, micro-mechanics
ABSTRACT
Miniaturization is a general trend in the microsystems industry, driving the design and manufactur-ing of smaller and smaller devices, structures, and parts. When the part’s dimensions are decreased to the same order of magnitude as the material’s characteristic microstructural length scales, signifi-cant changes in mechanical properties may occur, i.e. a so-called ”size-effect”. Traditional continuum mechanics approaches thereby loose their validity and predictive nature. This work analyses size ef-fects that are encountered first upon downscaling, including grain boundary efef-fects, free surface efef-fects, grain statistics effects. The separate influence of these first-order effects was carefully investigated us-ing the followus-ing experimental and numerical methodology. To minimize second phase particle and strain gradient effects, tensile experiments were conducted on very pure aluminum sheet material, a rel-evant material in microelectronics applications. The deformation behavior under uniaxial tension was analysed by probing specimens with a limited number of through-thickness grains across the width, whereby the amount of grains is reduced towards a single grain in the cross-section. Local mechanical properties and microstructure, e.g. grain size and orientation, were analyzed using nano-indentation, X-ray diffraction analysis, orientation imaging microscopy, and optical surface profilometry. In addition, a 3D dislocation-field strain gradient plasticity model was employed to analyze the intrinsic size effects by numerical simulations, using a grain size and texture as obtained from the aluminum test speci-mens. Using a straightforward Taylor type analysis, the physical mechanisms underlying the different size effects were further clarified. It is well known that the flow stress of a structure can be increased by decreasing the structure’s grain size, i.e. the Hall-Petch effect. However, this work shows that for miniaturized structures with a limited number of through-thickness grains a unique Hall-Petch relation does not exist, even though a grain boundary effect, i.e. increase in stress level (at a given strain) for de-creasing grain boundary area per unit volume, is clearly present. When the microstructure (and thus also the grain size) is kept constant upon miniaturization, the free surface per unit area increases causing the stress level of the structure to decrease. This free surface effect becomes especially significant for less
than 15 grains in one of the components dimension. In addition, it is found that grain statistics effects also contribute to observed weakening, due to insufficient compensation of the local (weaker) material properties by the surrounding material (i.e. grains), i.e. these local zones will increasingly dominate the overall mechanical properties. Grain statistics also significantly increase the statistical variation in mechanical properties for these small-sized structures, an effect that is especially important for the re-liability of miniature components. Finally, for structures with only a single grain in a cross-section, another size effect is observed; i.e. a small decrease in stress level is observed for decreasing cross-sectional area. The separate influence of these first-order effects as well as their interplay are explained in terms of the movement of the dislocations upon plastic flow.
