Yield Strength Enhancement in Multilayer Thin Films by Modulus Hardening
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YIELD STRENGTH ENHANCEMENT IN MULTILAYER THIN FILMS BY MODULUS HARDENING
JAMES E. KRZANOWSKI Mechanical Engineering Dept.,
University of New Hampshire,
Durham, NH 03824
ABSTRACT The modulus hardening mechanism for yield strength enhancement in multilayer materials is theoretically investigated. The multilayer composition profile used in the analysis has a general trapezoidal shape with allowance for two different layer thicknesses and two interface widths. The image force method is used to determine effective stresses on dislocations in the multilayer structure. Analytical expressions are derived for the effective stresses in terms of the shear elastic moduli. Calculations are carried out for representative composition profile shapes. It is found that the dislocation experiences the maximum effective stress when it is in the interface between layers, and that the effective stress increases dramatically with decreasing interface width. However, the effective stress is not strongly affected by either the multilayer wavelength or the relative thickness of the layers.
INTRODUCTION Materials with multilayer microstructures have generated considerable interest due to their novel physical and mechanical properties. The mechanical properties examined include plastic as well as elastic properties. The yield strength of multilayer structures has been examined in a number of studies [1-7]. These studies have shown that multilayer structures can exhibit enhanced yield strengths or hardness levels. The yield strengths generally increase with decreasing multilayer wavelength, although exceptions have been noted [3,6] in which yield strengths were independent of wavelength. The strengthening effect in multilayers has generally be attributed to one of two proposed mechanisms. First, multilayers with dissimilar lattice parameters can incorporate misfit dislocations at the interface between layers, impeding the motion of slip dislocations. If the misfit dislocations are sufficiently dense, the multilayer interfaces are effectively grain boundaries and the Hall-Petch relation can then be used to analyze hardening effects. The Hall-Petch analysis has been successfully applied to Cu-Ni [4,5] and Fe-Cu [4] multilayers. The second strengthening mechanism is modulus hardening, which is due to the variations in elastic modulus which can accompany composition variations. This mechanism was examined theoretically by Koehler [8], and the results have been used in several studies to explain observed strengthening effects [3,6]. The theory proposed by Koehler considered the effective stress on a dislocation as it approached a compositionally sharp interface, and neglected the effects of the surrounding interfaces. In a recent work by the present author [9], strengthening due to modulus hardening was theoretically analyzed for sinusoidal and symmetric (equal layer thickness) trapezoidal composition profiles with diffuse interfaces, and the effects of all multilayer interfaces in the structure were considered. It was found that the sharpness
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