Effective Indentation Modulus Research Articles

Nanoindentation measurements of anisotropic mechanical properties of single crystalline NMC cathodes for Li-ion batteries

Nickel manganese cobalt oxides (NMC) are the state-of-the-art cathode materials for Li-ion batteries. The layered lattice structure of NMC exhibits highly anisotropic strains upon Li intercalation, leading to particle fracture and interfacial delamination of the active particles from the conductive matrix. Such mechanical degradation becomes a crucial issue in the pursuit of high Ni-content and Co-free cathodes. Notably, the experimental information regarding the anisotropic mechanical properties of NMC cathodes is missing in the literature. In this study, we measure the stiffness constants of single crystalline NMC cathodes using environmental nanoindentation. The correlative measurements of the elastic stiffness and the lattice orientations allow us to fully determine the stiffness matrix. Furthermore, we compare the effective elastic indentation modulus, hardness, and fracture toughness of different NMC compositions. The complete information on the mechanical properties of NMC cathodes will enable accurate computational modeling and assist in designing and manufacturing durable rechargeable batteries.

In-situ synthesis of Ti5Si3-reinforced titanium matrix nanocomposite by selective laser melting: Quasi-continuous reinforcement network and enhanced mechanical performance

Titanium matrix nanocomposites (TMNCs) with quasi-continuously distributed Ti5Si3 reinforcements exhibit high material strength, good thermal stability, great tribological properties, and high fracture toughness. However, fabrication of such TMNCs via advanced additive manufacturing (AM) techniques has rarely been realized due to the presence of AM-induced large columnar grains and the cracking issue associated with the reinforcement coarsening. Here, we report a nanoparticle-mediated approach to in-situ fabricate nano-Ti5Si3 reinforced TMNC coatings by selective laser melting (SLM) of Ti powders and minor amount of SiC nanoparticles. Results showed that with the optimized SiC amount and SLM processing parameters, a crack-free and ultrahigh-strength TMNC consisted of near-equiaxed grain structure and nano-scale Ti5Si3 network at the grain boundaries was successfully produced. The optimized TMNC showed an ultrahigh surface microhardness of 706 VHN, 51.5% higher than that of SLM-fabricated SiC-free sample (466 VHN). Spherical nanoindentation results showed that the effective indentation modulus and indentation yield strength were improved by 62.6% and 57.2%, respectively. A more pronounced strain hardening phenomenon was also observed in the optimized TMNC. The dry sliding tests revealed that the wear rate was reduced by 70%, and the wear mechanism transferred from abrasion to adhesion.

Obesity alters the collagen organization and mechanical properties of murine cartilage

Osteoarthritis is a debilitating disease characterized by cartilage degradation and altered cartilage mechanical properties. Furthermore, it is well established that obesity is a primary risk factor for osteoarthritis. The purpose of this study was to investigate the influence of obesity on the mechanical properties of murine knee cartilage. Two-month old wild type mice were fed either a normal diet or a high fat diet for 16 weeks. Atomic force microscopy-based nanoindentation was used to quantify the effective indentation modulus of medial femoral condyle cartilage. Osteoarthritis progression was graded using the OARSI system. Additionally, collagen organization was evaluated with picrosirius red staining imaged using polarized light microscopy. Significant differences between diet groups were assessed using t tests with p < 0.05. Following 16 weeks of a high fat diet, no significant differences in OARSI scoring were detected. However, we detected a significant difference in the effective indentation modulus between diet groups. The reduction in cartilage stiffness is likely the result of disrupted collagen organization in the superficial zone, as indicated by altered birefringence on polarized light microscopy. Collectively, these results suggest obesity is associated with changes in knee cartilage mechanical properties, which may be an early indicator of disease progression.

Bayesian estimation of single ply anisotropic elastic constants from spherical indentations on multi-laminate polymer-matrix fiber-reinforced composite samples

In this paper, the application of a recently formulated two-step Bayesian framework to the estimation of effective anisotropic elastic constants of single plies within a multi-laminate polymer matrix composite is demonstrated, while using previously reported spherical indentation measurements within singular plies. Experimental spherical indentation measurements within the epoxy/fiber plies are inherently noisy due to local variation of the fiber volume fraction underneath the indenter. This paper demonstrates that the usage of a two-step Bayesian framework enables the extraction of reliable point estimates (and associated distributions) for the effective elastic constants from indentation modulus measurements conducted within single plies at different angles to the fiber orientations. The first step of the two-step Bayesian framework establishes the effective elastic indentation modulus of a single ply as a function of its intrinsic elastic stiffness parameters and the angle between the indentation direction and the fiber orientation using a database of suitable finite element simulations. The second step involves the calibration of the indentation measurements from a given set of multi-laminate samples to the reduced-order model established in the first step. The second step is accomplished by sampling the posterior distribution of the single ply elastic parameters via Monte Carlo Markov Chain methods. This new framework is demonstrated in this study for an IM7/977-3 carbon fiber/epoxy multi-laminate sample.

Impacts of maturation on the micromechanics of the meniscus extracellular matrix

To elucidate how maturation impacts the structure and mechanics of meniscus extracellular matrix (ECM) at the length scale of collagen fibrils and fibers, we tested the micromechanical properties of fetal and adult bovine menisci via atomic force microscopy (AFM)-nanoindentation. For circumferential fibers, we detected significant increase in the effective indentation modulus, Eind, with age. Such impact is in agreement with the increase in collagen fibril diameter and alignment during maturation, and is more pronounced in the outer zone, where collagen fibrils are more aligned and packed. Meanwhile, maturation also markedly increases the Eind of radial tie fibers, but not those of intact surface or superficial layer. These results provide new insights into the effect of maturation on the assembly of meniscus ECM, and enable the design of new meniscus repair strategies by modulating local ECM structure and mechanical behaviors.

Understanding indentation-induced elastic modulus degradation of ductile metallic materials

Noticeable degradation of the measured elastic moduli of ductile metals has been found in meso-/macro- indentation tests. Although this phenomenon has been exploited to estimate the fracture properties of ductile metallic materials, the mechanism of the indentation-induced damage is rarely studied. Finite element simulations show that the finite stiffness of an indentation system can cause a false degradation of the effective indentation modulus. However, the decay pattern is different from that due to the indentation damage. Through theoretical analysis and experimental measurements, it is shown that the elasticity degradation can be mainly attributed to the anisotropic damage caused by the shear deformation in the indentation test.

Longitudinal Study of the Effects of Environmental pH on the Mechanical Properties of Aspergillus niger.

The regulation of environmental pH is key to the health of an ecosystem, influencing the metabolic activity, growth, and development of organisms within it. Although pH values can be measured by a wide range of readily available technologies ranging from fluorescent dyes and nanosensors, these cannot reveal the history of environmental pH from before monitoring begins. This information is sometimes crucial for piecing together what has happened to an ecosystem, and our long-term goal is therefore to develop technologies capable of obtaining it. Here, we propose monitoring environmental pH over time by tracking mechanical properties of a common fungus. As a first step toward obtaining a time history of pH, we evaluate the effect of pH upon the effective indentation modulus of spores and hyphae of Aspergillus niger. We report that the indentation modulus of this phosphorus-solubilizing fungus, obtained through atomic force microscopy and nanoindentation, correlated with environmental acidity. We observed a significant, monotonic increase in moduli over the course of incubation in an acidic environment, but no change in moduli over time for incubation in a neutral environment. Results show promise for using our scheme to detect and track environmental pH over time, and more broadly for using a microorganism's mechanical properties as a biomarker for environmental detection.

Displacement fields and self-energies of circular and polygonal dislocation loops in homogeneous and layered anisotropic solids

There are large classes of materials problems that involve the solutions of stress, displacement, and strain energy of dislocation loops in elastically anisotropic solids, including increasingly detailed investigations of the generation and evolution of irradiation induced defect clusters ranging in sizes from the micro- to meso-scopic length scales. Based on a two-dimensional Fourier transform and Stroh formalism that are ideal for homogeneous and layered anisotropic solids, we have developed robust and computationally efficient methods to calculate the displacement fields for circular and polygonal dislocation loops. Using the homogeneous nature of the Green tensor of order −1, we have shown that the displacement and stress fields of dislocation loops can be obtained by numerical quadrature of a line integral. In addition, it is shown that the sextuple integrals associated with the strain energy of loops can be represented by the product of a pre-factor containing elastic anisotropy effects and a universal term that is singular and equal to that for elastic isotropic case. Furthermore, we have found that the self-energy pre-factor of prismatic loops is identical to the effective modulus of normal contact, and the pre-factor of shear loops differs from the effective indentation modulus in shear by only a few percent. These results provide a convenient method for examining dislocation reaction energetic and efficient procedures for numerical computation of local displacements and stresses of dislocation loops, both of which play integral roles in quantitative defect analyses within combined experimental–theoretical investigations.

Mechanical characterization of nanoporous materials by use of atomic force acoustic microscopy methods

We have used the atomic force acoustic microscopy (AFAM) method to determine the indentation modulus of nanoporous thin-film materials with ultralow values of dielectric permittivity (dielectric constant k < 2.4). The AFAM method is based on the contact mode of atomic force microscopy (AFM) and as such is able to characterize materials with high spatial resolution. The tested material was porous organosilicate glass with nominal porosity ranging from 27% to 40%. The values obtained for the indentation modulus varied from 4 to 7 GPa depending on the pore concentration. The values obtained for the indentation modulus by use of the AFAM method were in very good agreement with those determined by nanoindentation. In addition, a part of the AFAM results obtained for the sample with the highest porosity content showed dependence of the effective indentation modulus on the applied load. Preliminary data analysis suggests that the stress rate is the critical factor in triggering this particular mechanical response of the porous material.

Study of the nano-mechanical properties of human knee cartilage in different wear conditions

Osteoarthritis (OA) is a wear related disease that affects millions of people worldwide. Mechanical properties of cartilage surface play an important role in osteoarthritis initiation and progression. The objective of this study was to investigate the effective indentation modulus and its change in relation to the wear conditions of human knee cartilage. Following informed consent, samples were collected during orthopaedic surgery. Healthy and osteoarthritic cartilage samples at different OA stages were studied using atomic force microscopy. Unique to existing studies, the effective indentation moduli of the uppermost top surfaces of the healthy and osteoarthritic cartilage samples were measured. This study has shown that the modulus of the top surface changed significantly with wear severity progression. The findings have indicated that the effective indentation modulus measured at the nano-scale could be used to reveal changes in OA and to assist in understanding the wear process.

Nanoscale study of cartilage surfaces using atomic force microscopy

Articulating cartilage wear plays an important role in cartilage degeneration and osteoarthritis (OA) progression. This study investigated the changes of mechanical properties and surface roughness of sheep cartilages with wear progression at a nanometre scale. Young sheep's rear legs were subjected to a series of wear tests to generate worn cartilage samples to simulate the OA progression. Atomic force microscopy (AFM) was used to determine the effective indentation modulus and to measure the surface morphology of moist cartilage surfaces. The study has found that the mean effective indentation modulus values of worn cartilages were lower than that of healthy cartilage as the control sample. A medium-to-strong correlation between the effective indentation modulus values and the OA grades has been found. The relation between surface topography and effective indentation modulus values of the cartilage surfaces with OA progression was weakly correlated. The method established in this study can be implemented to investigate the effective indentation modulus values of clinical osteoarthritic cartilages and to assist in the understanding and assessment of OA.

Nanoindentation Study of Pop‐in Phenomenon Characteristics and Mechanical Properties of Sapphire (102) Crystal

The pop‐in behavior and mechanical properties of sapphire crystal vertically indented to its rhombohedral R (102) plane were investigated by nanoindentation using a Berkovich indenter. Effect of loading rate on pop‐in load and pop‐in extension width was observed within the indentation depth of h &lt; 120 nm. The indentation size effect (ISE) of hardness within an indentation depth of 60 nm was systematically analyzed using Nix‐Gao and Al‐Rub models. Our experiments provided the consistent evaluations of hardness (H = 27.5 GPa), true hardness (Htrue = 68.9 GPa) at the non‐ISE region and effective indentation modulus (M = 423 GPa) for the contact depth of hc &gt; 20 nm. Using the Hertzian contact theory, Schmid's law, and energy principle of indentation, the possible dominant slip system, which mainly contributed to the first pop‐in event when indented normal to the (102) plane, was estimated as {101} &lt;20&gt;. The distributions of corresponding resolved shear stress and principal stresses at the slip plane were also estimated.

Collective Mechanical Behavior of Multilayer Colloidal Arrays of Hollow Nanoparticles

The collective mechanical behavior of multilayer colloidal arrays of hollow silica nanoparticles (HSNP) is explored under spherical nanoindentation through a combination of experimental, numerical, and theoretical approaches. The effective indentation modulus E(ind) is found to decrease with an increasing number of layers in a nonlinear manner. The indentation force versus penetration depth behavior for multilayer hollow particle arrays is predicted by an approximate analytical model based on the spring stiffness of the individual particles and the multipoint, multiparticle interactions as well as force transmission between the layers. The model is in good agreement with experiments and with detailed finite element simulations. The ability to tune the effective indentation modulus, E(ind), of the multilayer arrays by manipulating particle geometry and layering is revealed through the model, where E(ind) = (0.725m(-3/2) + 0.275)E(mon) and E(mon) is the monolayer modulus and m is number of layers. E(ind) is seen to plateau with increasing m to E(ind_plateau) = 0.275E(mon) and E(mon) scales with (t/R)(2), t being the particle shell thickness and R being the particle radius. The scaling law governing the nonlinear decrease in indentation modulus with an increase in layer number (E(ind) scaling with m(-3/2)) is found to be similar to that governing the indentation modulus of thin solid films E(ind_solid) on a stiff substrate (where E(ind_solid) scales with h(-1.4) and also decreases until reaching a plateau value) which also decreases with an increase in film thickness h. However, the mechanisms underlying this trend for the colloidal array are clearly different, where discrete particle-to-particle interactions govern the colloidal array behavior in contrast to the substrate constraint on deformation, which governs the thickness dependence of the continuous thin film indentation modulus.

Mechanics of Nanoindentation on a Monolayer of Colloidal Hollow Nanoparticles

We explore the collective mechanical behavior of monolayer assemblies composed of close-packed arrays of hollow silica nanoparticles using a spherical nanoindentor. Seven types of well-defined hollow nanoparticles are studied with their radii ranging from 100 to 300 nm and shell thickness ranging from 14 to 44 nm. Micromechanical models reveal the underlying deformation mechanisms during indentation, where the consecutive contacting of the indentor with an increasing number of nanoparticles results in a nonlinear increase in the indentation force with penetration depth. Each contacted hollow nanoparticle successively locally bends, flattens, and then locally buckles. The effective indentation modulus of the monolayer film, which is obtained by a Hertzian fit to the experimental data, is found to be proportional to the elastic modulus of the nanoparticle shell material and scales exponentially with the ratio of particle shell thickness t to radius R to the power of 2.3. Furthermore, we find that for a constant film density with the same (t)/(R) of the constituent nanoparticles, smaller particles with a thinner shell can provide a higher effective indentation modulus, compared to their larger diameter and thicker shell counterparts. This study provides useful insights and guidance for constructing high-performance lightweight nanoparticle films and coatings with potential applications in tailoring stiffness and mechanical energy absorption.

Mechanomutable and reversibly swellable polyelectrolyte multilayer thin films controlled by electrochemically induced pH gradients

We present a new strategy to electrochemically control the swelling state and mechanical properties of a polyelectrolyte multilayer thin film. While a number of pH-responsive polymer films and hydrogels have been developed, biological systems typically will not tolerate substantial deviations in pH. Therefore, to apply such pH-responsive systems for biomedical or other sensitive applications, we developed an electrochemical approach to alter local pH, while maintaining a constant, mild, bulk pH. The polymer film investigated in this work comprises polyallylamine hydrochloride (PAH) and sulfonated polystyrene (SPS) assembled at high pH (>9.0), which is known to exhibit a large pH-induced swelling transition; however, relatively extreme bulk pH values (pH < 4 to swell, and pH > 10.5 to deswell) are required to manipulate the film. Here, we apply negative electric potentials to gold electrodes coated with the film; the potential induces the reduction of dissolved oxygen, which generates hydroxide ions at the electrode surface and raises the local pH. The in situ swelling state and mechanical properties of the film have been probed with a number of techniques. Overall, we have attained reversible 300% volume changes in the polymer thin films, and have reversibly altered the mechanical properties over an order of magnitude (shear modulus between 1.9 MPa and 230 kPa, loss modulus between 620 kPa and 92 kPa, and effective indentation modulus between 19.2 MPa and 3.16 MPa). We maintain that electrochemical control over local pH is a promising strategy to manipulate pH-responsive polymer systems for biomedical and other applications.

Anisotropic design of a multilayered biological exoskeleton

Biological materials have developed hierarchical and heterogeneous material microstructures and nanostructures to provide protection against environmental threats that, in turn, provide bioinspired clues to improve human body armor. In this study, we present a multiscale experimental and computational approach to investigate the anisotropic design principles of a ganoid scale of an ancient fish,Polypterus senegalus,which possesses a unique quad-layered structure at the micrometer scale with nanostructured material constituting each layer. The anisotropy of the outermost prismatic ganoine layer was investigated using instrumented nanoindentations and finite element analysis (FEA) simulations. Nanomechanical modeling was carried out to reveal the elastic-plastic mechanical anisotropy of the ganoine composite due to its unique nanostructure. Simulation results for nanoindentation representing ganoine alternatively with isotropic, anisotropic, and discrete material properties are compared to understand the apparent direction-independence of the anisotropic ganoine during indentation. By incorporating the estimated anisotropic mechanical properties of ganoine, microindentation on a quad-layered FEA model that is analogous to penetration biting events (potential threat) was performed and compared with the quad-layered FEA model with isotropic ganoine. The elastic-plastic anisotropy of the outmost ganoine layer enhances the load-dependent penetration resistance of the multilayered armor compared with the isotropic ganoine layer by (i) retaining the effective indentation modulus and hardness properties, (ii) enhancing the transmission of stress and dissipation to the underlying dentin layer, (iii) lowering the ganoine/dentin interfacial stresses and hence reducing any propensity toward delamination, (iv) retaining the suppression of catastrophic radial surface cracking, and favoring localized circumferential cracking, and (v) providing discrete structural pathways (interprism) for circumferential cracks to propagate normal to the surface for easy arrest by the underlying dentin layer and hence containing damage locally. These results indicate the potential to use anisotropy of the individual layers as a means for design optimization of hierarchically structured material systems for dissipative armor.