Understanding Size Effects in Small Scale Deformation: A Statistical Perspective

Recent experimental observations of micro-compression / tension tests indicate that as the size of test specimen decreases the yield strength increases. This raises a fundamental question: Why is smaller stronger? Is there a fundamental relationship between the size of a specimen and its intrinsic strength? This simple question pushes the limit of the current understanding of the physical mechanisms underlying material deformation, especially at small scales. In order to explain the experimental observations of the strength of small specimens containing a limited number of dislocations, a simple statistical model is developed. Two different types of randomness are introduced, viz., randomness in the spatial location of dislocations and randomness in the stress needed to activate them. For convenience, the randomness in the activation stress is modeled by assigning a random Schmid factor to the dislocations. In contrast to the previous stochastic models, the current model not only predicts the yield strength in the presence of dislocations but also in their absence. Furthermore, the model has the capability to predict the scatter in the yield strength in addition to the mean. Monte Carlo simulations are also performed for comparison. Interestingly, the model adds credence to the notion that “smaller is stronger” from a purely statistical point of view. The model is found to quantitatively explain the yield strength and scatter in micro-compression / tension tests of Mo-alloy fibers using dislocation densities and arrangements measured by TEM. Furthermore, the model is extended to spherical indentation pop-in which is an analogous size dependent problem in small scale mechanics. In this case, the model predicts the load and maximum shear stress at pop-in as a function of indenter radius and is found to closely match the experimental results on single crystal molybdenum using a dislocation density estimated by micro-focus x-ray techniques. In summary, the current work provides possible explanations for the strength and scatter in strength of small specimens from a purely statistical perspective

Measurement of hardness and elastic modulus by depth sensing indentation: Further advances in understanding and refinements in methodology

Depth sensing indentation technique has been widely used to measure small scale mechanical properties over the years. Starting from the seminal work of Oliver & Pharr [1], there have been many improvements / modifications to the test methodology and also significant advances in measurement electronics / testing instrumentation. These advancements provide opportunities to not only develop novel testing capabilities but also further improve the precision and accuracy of the most common measurement parameters – hardness and elastic modulus. In this regard, this work presents a comprehensive study on the various steps involved in a typical depth sensing indentation test, viz., surface approach, surface detection, load-time history including superimposing an oscillatory force on broad band load, unloading and drift rate measurement. The effect of each of these steps on the accuracy and precision of the hardness and elastic modulus measurement will be discussed with specific focus on frequency specific testing techniques such as continuous stiffness measurement. The effect of the instrument’s measurement time constants and dynamic parameters such as mass, spring constant and damping coefficient during different steps of an indentation test and thereby on the hardness and elastic modulus will be presented. A simple model is developed to simulate a depth sensing indentation test that incorporates the material and instrumentation parameters to help visualize the overall process and provide new insights for pushing the limits of the currently available instrumentation for improved precision and accuracy. This involves performing tests beyond the traditional boundaries of parameter space such as increased oscillation amplitude, strain rate, oscillation frequency, etc. For instance, if the indentation strain rate gets high compared to the oscillation frequency, inaccuracies can occur. This work presents the critical experimental parameters and the associated first order corrections for the potential errors. The model predictions and corrections are validated on different classes of materials. Finally, guidelines for measuring hardness and elastic modulus using a depth sensing indentation test with significantly improved precision and accuracy within the limitations of the currently available instrumentation will be discussed. [1] Oliver & Pharr, Journal of Materials Research, 7(6),1992

Measurement of hardness and elastic modulus by depth sensing indentation: Improvements to the technique based on continuous stiffness measurement

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Wide dynamic range 2-D nanoindentation: Friction and partial slip at contacts

A new nanomechanical testing system is described. It provides the same force controlled displacement sensing capability as nanoindentation, but now with two completely separated orthogonal axes. Load modulation enables direct determination of contact area and stiffness, both lateral and vertical, along with energy losses from the phase shifts. Two features in particular, wide dynamic ranges of several orders of magnitude of stiffness and a very high degree of mechanical separation (low crosstalk) between the axes, distinguish the technique from AFM. AFM is one of the few techniques to date to investigate tribological single asperity contacts but its mechanical limitations make it difficult to discern the underlying mechanisms. With this new technique, the evolution of a contact under 2-D stresses from deformation-free atomistic scale to initial plasticity along with the associated changes in geometry, can be monitored. Results will be presented showing that unlike in elastic contacts, Mindlin partial slip does not occur immediately under lateral stress in plastically deformed contacts. The evolution of contact area in the initial stages of sliding in the presence of plastic flow will be described, and resembles the predictions of classical Tabor and Johnson models. It will be shown that energy dissipation measured from phase shift of a modulating signal is largely due to interfacial friction rather than volumetric deformation. Prospects for further studies using both shear and normal loading will be discussed

The influence of heat treatment on the microstructural, mechanical and corrosion behaviour of cold sprayed SS 316L coatings

The present study evaluates the response of cold sprayed SS 316L coatings on mild steel substrate to aqueous corrosion in a 0.1 N HNO3 solution as determined using polarization tests. The corrosion behaviour of the SS 316L coating was studied not only in the as-coated condition, but also after heat treatment at 400, 800 and 1,100 °C. Heat treatment reduced the porosity, improved inter-splat bonding, increased the elastic modulus and more importantly increased the corrosion resistance of the cold sprayed SS 316L coating

Nanoindentation at elevated temperatures

Relating the creep response observed with high temperature instrumented indentation experiments to macroscopic uniaxial creep response is of great practical value. In this review, we present an overview of various methods currently being used to measure creep at small scales with instrumented indentation, with a focus on geometrically self-similar indenters, and their relative merits and demerits from an experimental perspective. A comparison of the various methods to use those instrumented indentation results to predict the uniaxial power law creep response of a wide range of materials (stress exponent of 1 to 8), will be presented to assess their validity. The interplay of size dependent hardness effects, strain rate effects and temperature effects will also be discussed. The extension of rapid testing and mapping techniques to high temperatures will also be demonstrated. Figure 1 shows a map of hardness vs position in a carbide containing steel at 300 degrees C. These techniques are extended to stress exponent and pre-exponential maps determined at high temperatures. Please click Additional Files below to see the full abstract

Mapping of mechanical properties at microstructural length scale in WC-Co cemented carbides: Assessment of hardness and elastic modulus by means of high speed massive nanoindentation and statistical analysis

This paper studies the correlation between the microstructure and the mechanical properties at the nanometric length scale of individual WC grains as well as the metallic cobalt binder in cemented carbide systems. The local crystallographic orientation has been determined by electron backscattered diffraction and the microstructural analysis has been performed using field emission scanning electron microscopy. Small-scale hardness and elastic modulus have been assessed by means of high speed massive nanoindentation and subsequent statistical analysis. The attained mechanical property mappings present a clear correlation between local hardness and stiffness with chemical nature for each constitutive phase as well as with the crystallographic orientation for the WC particles. Besides expected findings associated with individual phases, such as clear anisotropy of the ceramic phase (basal plane being harder and stiffer than the prismatic one) and relatively high flow stress for constrained binder, the protocol implemented provides novel information on local mechanical response at interfaces between ceramic particles with different orientations as well as regions within the metallic cobalt binder close to the WC-Co interface.Peer ReviewedPreprin

A novel nanoindentation protocol to characterize surface free energy of superhydrophobic nanopatterned materials

Abstract Surface Free Energy (SFE) has become a relevant design parameter to produce materials and devices with controlled wettability. The non-destructive measurement of SFE in nanopatterned super-hydrophobic hard surfaces is a challenge in both research and industry since in most cases time-consuming contact angle measurements are not feasible. In this work, we present a novel nanoindentation based method for the measurement of pull-off adhesive forces by carefully controlling environmental and instrumentation issues. The method is found to measure SFE over five orders of magnitude, covering hydrophilic to super-hydrophobic surfaces, and has been validated with contact angle measurements. Its limitations and shortcomings are critically discussed, with a specific focus on the experimental issues that could affect the reliability and reproducibility of the results. Finally, the potential applications of the newly developed methodology include fast non-destructive mapping of SFE over heterogeneous surfaces with spatially controlled wettability. Graphic abstrac

Ultra High Strain Rate Nanoindentation Testing

Strain rate dependence of indentation hardness has been widely used to study time-dependent plasticity. However, the currently available techniques limit the range of strain rates that can be achieved during indentation testing. Recent advances in electronics have enabled nanomechanical measurements with very low noise levels (sub nanometer) at fast time constants (20 µs) and high data acquisition rates (100 KHz). These capabilities open the doors for a wide range of ultra-fast nanomechanical testing, for instance, indentation testing at very high strain rates. With an accurate dynamic model and an instrument with fast time constants, step load tests can be performed which enable access to indentation strain rates approaching ballistic levels (i.e., 4000 1/s). A novel indentation based testing technique involving a combination of step load and constant load and hold tests that enables measurement of strain rate dependence of hardness spanning over seven orders of magnitude in strain rate is presented. A simple analysis is used to calculate the equivalent uniaxial response from indentation data and compared to the conventional uniaxial data for commercial purity aluminum. Excellent agreement is found between the indentation and uniaxial data over several orders of magnitude of strain rate