Experimentally measured cyclic indentation load-displacement curve for a 1 μm-thick pure Al film on a Si substrate. 12
Schematic showing the Al thin film above a Si substrate and the boundary conditions used in the axisymmetric model. The left boundary is the symmetry axis. The entire specimen is 40 μm in lateral span (radius) and 43 μm in height. The Al film is 2 μm thick.
Representative uniaxial cyclic stress-strain response following the elastic-viscoplastic constitutive model used in this study. The loading is under a stress rate of 2000 MPa/s, with the maximum and minimum stresses being 240 and 24 MPa, respectively.
Simulated indentation load–displacement curve during the first two cycles, when the Al film is assumed to be rate-independent.
Simulated indentation load–displacement curve during the first two cycles, when the rate-dependent elastic-viscoplastic model is incorporated into the analysis.
Contour plots of equivalent plastic strain for the case of a homogeneous Al film (a) at the peak indentation load after the first loading phase, (b) when the load is reduced to 10% of the peak load after the first unloading, and (c) at the peak loading during the second cycle. The white circular marks in (a) and (b) are used for highlighting the locations of material points used in tracking the deformation history as presented in Figs. 7 and 8 .
Evolution of (a) equivalent plastic strain and (b) several stress components, in an element highlighted in Fig. 6(a) , during the first two cycles of deformation history. (VM: von Mises effective stress.)
Evolution of (a) equivalent plastic strain and (b) several stress components, in a second element highlighted in Fig. 6(b) , during the first two cycles of deformation history. (VM: von Mises effective stress.)
Simulated ten full cycles of indentation load-displacement response.
Strain rate hardening response (yield ratios at different plastic strain rates) of Al used in the viscoplastic model.
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