A. A. Elmustafa

Nanoindentation and the indentation size effect: Kinetics of deformation and strain gradient plasticity

Abstract A study of the indentation size effect (ISE) in aluminum and alpha brass is presented. The study employs rate effects to examine the fundamental mechanisms responsible for the ISE. These rate effects are characterized in terms of the rate sensitivity of the hardness, ∂ H/ ∂ ln e eff , where H is the hardness and e eff is an effective strain rate in the plastic volume beneath the indenter. ∂ H/ ∂ ln e eff can be measured using indentation creep, load relaxation, or rate change experiments. The activation volume V ∗ , calculated based on ∂ H/ ∂ ln e eff which can traditionally be used to compare rate sensitivity data from a hardness test to conventional uniaxial testing, is calculated. Using materials with different stacking fault energy and specimens with different levels of work hardening, we demonstrate how increasing the dislocation density affects V ∗ ; these effects may be taken as a kinetic signature of dislocation strengthening mechanisms. We noticed both H and ∂ H/ ∂ ln e eff (V ∗ ) exhibit an ISE. The course of V ∗ vs. H as a result of the ISE is consistent with the course of testing specimens with different level of work hardening. This result was observed in both materials. This suggests that a dislocation mechanism is responsible for the ISE. When the results are fitted to a strain gradient plasticity model, the data at deep indents (microhardness and large nanoindentation) exhibit a straight-line behavior closely identical to literature data. However, for shallow indents (nanoindentation data), the slope of the line severely changes, decreasing by a factor of 10, resulting in a “bilinear behavior”.

Grain-size-dependent thermal conductivity of nanocrystalline yttria-stabilized zirconia films grown by metal-organic chemical vapor deposition

A grain-size-dependent reduction in the room-temperature thermal conductivity of nanocrystalline yttria-stabilized zirconia is reported for the first time. Films were grown by metal-organic chemical vapor deposition with controlled grain sizes from 10 to 100 nm. For grain sizes smaller than approximately 30 nm, a substantial reduction in thermal conductivity was observed, reaching a value of less than one-third the bulk value at the smallest grain sizes measured. The observed behavior is consistent with expectations based on an estimation of the phonon mean-free path in zirconia.

Flexural-hinge guided motion nanopositioner stage for precision machining: finite element simulations

Finite element analysis has been used to study the behavior of flexural-hinge guided- motion nanopositioning stages designed for use in precision machining. The primary criteria of such nanopositioners are a high stiffness and large load carrying ability. Both static loading and modal frequency analysis are performed. A procedure is developed by which we can redesign and reanalyze the model while simulating the performance of the nanopositioner. Modification of dimensions enables us to control and optimize resonant frequency, displacement, stresses, and force to be applied to the hinges to achieve the desired response of the positioner and the positioner motion.

Analysis of indentation creep

Finite element analysis is used to simulate cone indentation creep in materials across a wide range of hardness, strain rate sensitivity, and work-hardening exponent. Modeling reveals that the commonly held assumption of the hardness strain rate sensitivity ( m H ) equaling the flow stress strain rate sensitivity ( m σ ) is violated except in low hardness/modulus materials. Another commonly held assumption is that for self-similar indenters the indent area increases in proportion to the (depth)2 during creep. This assumption is also violated. Both violations are readily explained by noting that the proportionality “constants” relating (i) hardness to flow stress and (ii) area to (depth)2 are, in reality, functions of hardness/modulus ratio, which changes during creep. Experiments on silicon, fused silica, bulk metallic glass, and poly methyl methacrylate verify the breakdown of the area-(depth)2 relation, consistent with the theory. A method is provided for estimating area from depth during creep.

Size-dependent hardness in annealed and work hardened α-brass and aluminum polycrystalline materials using activation volume analysis

Abstract A study of the size-dependent hardness in aluminum and α-brass is presented. The study employs rate-effects to examine the fundamental mechanisms responsible for the indentation hardness size dependence (effect), or (ISE). These rate effects are characterized in terms of the rate sensitivity of the hardness, ∂ H /∂ln e eff , where H is the hardness and e eff is an effective strain rate in the plastic zone beneath the indenter. ∂ H /∂ln e eff is measured using indentation creep, load relaxation, and rate change experiments. ∂ H /∂ln e eff is used to calculate the activation volume, V *; activation volume data measured using conventional uniaxial testing are compared with activation volume data measured using nanoindentation. The data for α-brass when plotted V * vs. H (hardness) or σ (flow stress), extrapolated into literature data from conventional uniaxial testing, while the aluminum data suffered an offset. We propose some mechanisms for this offset. Using V * formalism, we demonstrate using materials with different stacking fault energy (SFE) and specimens with different levels of work hardening how increasing the dislocation density affects V *; these effects may be taken as a kinetic signature of dislocation strengthening mechanisms. We depicted an ISE in both H and ∂ H /∂ln e eff ( V *). The trend of V *-vs.- H as a result of the ISE is consistent with the trend of testing specimens with different levels of work hardening. This indicates that a dislocation mechanism drives the ISE.

Pile-up/sink-in of rate-sensitive nanoindentation creeping solids

Pile-ups and sink-ins influence the measurement of the contact area in indentation hardness testing particularly when the indent size becomes significantly small, i.e. in nanoindentation. In this paper, we study the effect of strain rate and work hardening on pile-ups and sink-ins of creeping solids during the indentation process. We use a strain hardening creeping constitutive relation available in the ABAQUS finite element analysis commercial code. The simulations were performed for a work hardening exponent, χ = ∂ ln σ/∂ ln e of 0.1–0.3 and a strain rate sensitivity of von Mises stress, of 0.04–0.16. We report that strain rate sensitivity and work hardening influence the measure of pile-ups and sink-ins. It is reported in the literature that rate-insensitive materials undergo sink-in with the increase in the work hardening exponent and tend to pile-up in the absence of work hardening. In this research for rate-sensitive materials, we observe similar behavior but the effect is less profound. We also depict similar results for pile-up.

Stacking fault energy and dynamic recovery: do they impact the indentation size effect?

Abstract Aluminum, a high stacking fault energy (SFE) material and α-brass, a low SFE material were tested for the indentation size effect (ISE) using a combination of microhardness (high load) and nanoindentation (low load). Four samples from each material were tested; annealed electropolished, annealed mechanically polished, work-hardened electropolished, and work-hardened mechanically polished. The micro and nano indentations were made using a Vickers and a Berkovitch diamond indenter tips with indentation loads between 0.1–3 (microindentations) and 10−4–10−2 N (nanoindentations), respectively. Based on areas measured using optical and scanning electron microscopy in addition to contact stiffness, it is found that the calculated nanohardness increases monotonically with decreasing load or depth of indentation. The work-hardened samples are harder than the annealed ones except for aluminum at shallow indents where it is not possible to distinguish between differences in hardness. All eight samples regardless of the SFE, rate and intensity of cross-slip and dislocation climbing rates (dynamic recovery), and level of prior work hardening of the material, explicitly exhibited an ISE. The magnitude of the ISE is not influenced by SFE, dynamic recovery, or prior level of work hardening. The data are found to behave linearly consistent with the Strain Gradient Plasticity model (SGP) for micro and deep nanoindentations; the shallow nanoindentation data deviated into a second linear behavior constituting what we term a ‘bilinear behavior’.

Mechanical and structural characterization of atomic layer deposition-based ZnO films

Zinc oxide thin films were deposited by atomic layer deposition (ALD). The structural and mechanical properties of the thin films were investigated by x-ray diffraction, transmission electron microscopy, atomic force microscopy, and nanoindentation. Diethyl zinc was used as the chemical precursor for zinc and water vapor was used as the oxidation agent. The samples were deposited at 150 °C and at a pressure of 2.1 × 10−1 Torr in the ALD reactor. A growth rate of 2 A per cycle was calculated in the ALD process window. The Nano Indenter XP was used in conjunction with the continuous stiffness method in depth control mode in order to measure and to analyze the mechanical properties of hardness and modulus of ALD ZnO thin film samples. For comparison, we benchmarked the mechanical properties of single crystal bulk ZnO samples against those of our ALD ZnO thin films.

Activation analysis of deformation in evaporated molybdenum thin films

Using nanoindentation, we investigate hardening mechanisms in steered arc (SA) evaporated and electron-beam (EB) evaporated molybdenum thin films. Both films have columnar grains, with the column diameters ranging between 22 and 170 nm in the SA films and 30 and 40 nm in the EB films. The Hall–Petch relation is extended out to hardness values between 6 and 12 GPa. Analysis of nanoindentation creep data (creep, load relaxation, and rate change) reveals that, in the SA films, thermally activated glide is rate controlling, and that grain size has little effect on the underlying rate processes even down to 22 nm. There is evidence based on x-ray diffraction (and supported by the literature) that the EB films contain high densities of interstitial loops resulting from argon ion bombardment during deposition. The analysed creep data indicate that these loops affect the thermal activation of dislocations.

A numerical study on pile-up in nanoindentation creep

In this paper, we simulate materials of variable hardness, work hardening exponent, χ = ∂1nσ/∂1ne of 0.1?0.3 and a strain rate sensitivity of von Mises stress, vσ = ∂1nσ/∂1ne of 0.08?0.16 to estimate pile-ups and sink-ins during indentation creep and compare the results with literature data. We report that materials pile-up for vΗ/vσ ≥ 1.0 and sink-in for vΗ/vσ < 1.0, vσ is the strain rate sensitivity of the hardness. vΗ/vσ approaches 1 for small Η/E*, i.e., soft materials and deformation is dominated by pile-up, whereas when vΗ/vσ approaches 0 for large Η/E* corresponds to purely elastic deformation which is apparently dominated by sink-in in a manner prescribed by Hertzian contact mechanics.