Meet Karim

Name: Karim R. Mahmoud Gadelrab
Research interest: Nanoidentation
Email: kgadelrab@masdar.ac.ae

Research Summary

In recent years, Nanoindentation technique has evolved to become a major tool to mechanically characterize nanoscale materials. While advances in electronics have significantly enhanced device accuracy, the theory employed to extract material properties still suffers from inaccuracies at shallower indentation depth.

Nanoindentation analysis relies on Sneddon’s solution to indentation problems. Sneddon based his solution on two main assumptions namely: the tip is rigid with perfect geometry and the indented material is linear elastic isotropic half space. Unfortunately, these assumptions can hardly be met in real life experiments. Tip rounding is a major form of tip imperfection.

Neglecting this kind of imperfection leads to erroneous estimation of results especially at indentation depth comparable to the value of the tip radius, typical for nanostructures. This thesis presents a closed form solution for a blunted cone indenting linear elastic half space. The derivation is compared to 2D finite element analysis FEA. Based on the numerical results, we derive a new form for the reduced modulus equation derived by Oliver and Pharr [1] to account for tip rounding. This proposed model is verified experimentally on fused silica and is further extended to be applied on thin films.

Fused silica deformation is simulated using FE method. To account for fused silica densification during indentation, a linear Drucker Prager constitutive equation is implemented. The FE simulation is verified experimentally using force indentation curves and Raman microspectroscopy densification maps.

Furthermore we develop a numerical assisted framework to interpret indentation data. The framework is based on the use of an appropriate constitutive equation for the plastic deformation in finite element analysis and atomic force microscopy tip scans directly imported to FE code. For the first time, we are able to simulate fused silica indentation without any uncertainties related to tip geometry. We prove that our framework is capable of treating nanoindentation data to provide accurate material properties excluding any correction factors or unrealistic assumptions.

Meshed solid model.
(a) Finer mesh at the point of contact
(b) Indenter tip roundness The cylindrical substrate size is (D*t=2*2 µm2) and the indentation depth is in general less than 10% of the substrate height as recommended by Fischer [48] to achieve conversion and to avoid interaction with substrate boundaries.

Berkovich tip scan obtained at 512×512 scanning resolution with tip speed of 6.25 μm/s.

Strain distribution for a Berkovich indenter. Deformation shape is different from the expected triangular shape.

Elastic indentation with a perfectly sharp cone to 60nm depth. The point of highest stress is found just under the apex. (Stresses are in N/nm2)

Elastic indentation with a blunted cone (R=100nm) to 60nm. The highest stress region moves beneath the surface. (Stresses are in N/nm2).

Elastic indentation with a blunted Berkovich tip (R=100nm) to 60nm (0.06 µm). The stress is not symmetric with regions of higher stress under the edges. Arrows show material pile up at the edges and sink in at the face. (Stresses are in N/µm2)

Comparison between the numerical densification maps in percentages (on the right side) and the experimental results obtained from Raman Microspectroscopy (on the left side)[34, 35]. The +2.8% is an expansion in underlying material. This can be attributed to the elastic recovery of the material after load removal.

An AFM scan for Tip
(A) and the corresponding FEA generated surface. The scan shows the sharpness on the tip. (b) An old tip
(B) scan and the corresponding FEA generated surface. The scan shows the bluntness of the tip and residuals sticking to its surface.