Sink-in Effects Research Articles

Numerical study on the surface morphology evolution and hardness during the spherical indentation of copper with plastic behavior described by different stress-strain relationships

Spherical indentation on flat surfaces of metallic materials is a very simple and useful test for evaluating mechanical properties. FEM-based simulations have been extensively employed to study pile-up and sink-in effects during indentation process for materials which have plastic behavior described by Hollomon’s power law, where the strength coefficient K is calculated by the continuity condition. In the present numerical study, the stress-strain data of OFHC copper was fitted by three relationships: Voce, Hollomon and continuity-based Hollomon. Then sequential simulations of frictionless compression and ball-indentation tests were carried out, resulting in indentation load-depth curves of workpieces at different hardening levels. These load-depth curves were analyzed to determine the Meyer’s index, the pile-up/sink-in effects, and the Brinell Hardness of each workpiece. The results were compared to literature models and experimental data. The different mechanical behaviors of the Voce- and Hollomon-driven materials during indentation were explained on basis of competition between elastic and plastic deformations along the process. When using Voce’s relationship, the simulated Hardness Brinell curve agreed perfectly with experimental data obtained by Tabor (1951) for annealed and work-hardened copper, and the predicted sink-in for annealed copper agreed very well with experimental data from Campbell et al. (2018). The numerical and mathematical model proved be consistent and results indicate that plastic behavior of copper under indentation test is better described by the three-parameters Voce’s hardening law.

Comparison between conventional Vickers hardness and indentation hardness obtained with different instruments

Abstract An extensive comparison between the conventional Vickers hardness at 500 mN and indentation hardness measured with Vickers indenters at 500 mN is presented for up to 20 different materials and for three different instruments. Additionally, the indentation modulus is compared to Young’s modulus, which was measured with alternative methods or taken from the literature. It is shown that the agreement between the results from depth-sensing indentation and the reference values can be improved by additional corrections, for the calculation of the indentation area. With corrections the mean hardness difference to the Vickers hardness reference as average of all investigated materials can be reduced to about 10 % although disturbing pile-up or sink-in effects can still not be considered. For the modulus, the mean difference was only about 6 %.

Conversion between Vickers hardness and nanohardness by correcting projected area with sink-in and pile-up effects

The Vickers hardness test has been widely used for neutron-irradiated materials and nanoindentation for ion-irradiated materials. Comparing the Vickers hardness and nanohardness of the same materials quantitatively and establishing a correlation between them is meaningful. In this study, five representative materials—pure titanium (Ti), nickel (Ni), tungsten (W), 304 coarse-grained stainless steel (CG-SS) and 304 nanocrystalline austenitic stainless steel (NG-SS)—are investigated for comparison. The results show that the relationship between Vickers hardness and nanohardness does not conform to a mathematical geometric relationship because of sink-in and pile-up effects confirmed by finite element analysis (FEA) and the results of optical microscopy. Finally, one new method was developed by excluding the effects of sink-in and pile-up in materials. With this improved correction in the projected area of the Vickers hardness and nanohardness, the two kinds of hardness become identical.

A new nanoindentation creep technique using constant contact pressure

Abstract

Contact geometry during indentation of a sphere into an elastoplastic half-space

The indentation of a sphere into an elastoplastic half-space is considered, which is accompanied by pile-up / sink-in effects, extrusion of material around a sphere (formation of a bulk) and elastic sinking of the material. The evolution of studies of the indicated phenomena is shown. Based on the similarity of the deformation characteristics, expressions are obtained for determining the indentation depth, the depth of the residual crater, and the contact depth depending on the degree of loading. In this case, the influence of the characteristics of the hardened material — the yield strength and the hardening exponent — were taken into account. The radial boundary of the bulk is determined from the volume of the displaced material. Expressions are obtained for describing the profile of a loaded and unloaded crater.

Electrochemically synthesized amorphous and crystalline nanowires: dissimilar nanomechanical behavior in comparison with homologous flat films.

The effects of constrained sample dimensions on the mechanical behavior of crystalline materials have been extensively investigated. However, there is no clear understanding of these effects in nano-sized amorphous samples. Herein, nanoindentation together with finite element simulations are used to compare the properties of crystalline and glassy CoNi(Re)P electrodeposited nanowires (ϕ ≈ 100 nm) with films (3 μm thick) of analogous composition and structure. The results reveal that amorphous nanowires exhibit a larger hardness, lower Young's modulus and higher plasticity index than glassy films. Conversely, the very large hardness and higher Young's modulus of crystalline nanowires are accompanied by a decrease in plasticity with respect to the homologous crystalline films. Remarkably, proper interpretation of the mechanical properties of the nanowires requires taking the curved geometry of the indented surface and sink-in effects into account. These findings are of high relevance for optimizing the performance of new, mechanically-robust, nanoscale materials for increasingly complex miniaturized devices.

Mechanical behavior of hard amorphous Si–C–N thin films

Completely hard amorphous Si–C–N films were prepared by electron cyclotron resonance microwave plasma assisted chemical vapor deposition and characterized by atomic force microscopy and nanoindentation. In contrast to common findings of sink-in effects for hard films on soft substrates, anomalous pile-up effects were observed in such kinds of hard films. Inherently different from the traditional measurements of hardness, which are taken from the residual impression after unloading, load–displacement curves from nanoindentation measurements reveal the feature of a large elastic deformation based on the evaluation of the total work and the elastic work. The reduced modulus shows an approximately linear relationship with the measured hardness, while no linear relation can be extracted for the energy dissipation and the ratio of hardness and Young modulus, H/E. Mechanical behaviors of Si–C–N films measured by the Oliver and Pharr method match well with the fitted data from the modified King's model within the investigated range of the indentation depth.

Determination and Relaxation of Residual Stress in 2024 Al-30 vol.% Magnesium Borate Whisker Composites

Residual stresses in 30 vol.% magnesium borate whisker-reinforced 2024 aluminum matrix composites have been determined by a nanoindentation method which takes into consideration pile-up and sink-in effects on indentation contact depth. Owing to the thermal mismatch and the large difference in elasticity modulus between the Al matrix and MBO whiskers, tensile residual stress was introduced to Al matrix material during fabrication. It was found that the solution treatment reduced the tensile residual stress by producing interfacial component and dislocations in the composites. Cryogenic cooling released the stress via reversing the tensile residual stress to compression in the matrix, which was more effective than solution treatment to release the tension stress in the composites. The combination of the solution treatment and the cryogenic cooling provided the most effective procedure to release the residual stress in the composites, which reduced the tensile residual stress from 232.6 to 56.5 MPa, i.e., 76% reduction. Meanwhile, no cracks were observed in the composite when processed with such sudden thermal shocking.

An expanding cavity model incorporating pile-up and sink-in effects

Abstract

Calculation of the Mechanical Properties of FeB Layer's by Finite Element Method

Surface treatments of engineering materials are important for serviceable engineering components. One of the thermo-chemical surface treatments of steel based materials is the boriding process. In this study, low alloy steel substrates were borided by pack boriding process at 900 °C. Experimental indentation tests were conducted on Dynamic Ultra-micro Hardness test machine, under applied peak loads of 800 mN, 1000 mN, 1200 mN and 1400 mN. To get the mechanical properties of FeB layers, the resulting load–unload test data of the samples obtained from the experimental indentation tests were analyzed and curve-fitted in Kick’s and Meyer’s law for the loading and the unloading part of the load-unload curve respectively. Then, a set of analytical functions that take the pile-up and sink-in effects into account during instrumented sharp indentation were solved using numerical methods. These analytical functions were defined within an identified representative plastic strain, εr, for the Vickers indenter geometry as a strain level that allows for the description of the indentation loading response independent of strain hardening exponent, n. The mechanical characterization of samples, finite element modeling was applied to simulate the mechanical response of FeB layer on low alloy steel substrate by using ABAQUS software package program.

A Model for the Calculation of Mechanical Properties of Hydroxyapatite Coatings on Ti6Al4V Substrate Using Finite Element Methods

The scope of this study is to find out yield curve on the coating-substrate system of hydroxyapatite (HA) by finite element modeling. With this regard, Hydroxyapatite (HA) coatings were successfully formed on Ti6Al4V substrates by using biomimetic technique. Experimental indentation tests were conducted on Dynamic Ultra-micro Hardness test machine. In finite element modeling (FEM), mechanical properties of coatings were determined by using ABAQUS software package. This numerical study was carried out using an axisymmetric FEM model. To calculate the mechanical properties of coating, the resulting load–unload test data of the samples obtained from the experimental indentation tests were analyzed and curvefitted in Kick’s and Meyer’s law for the loading and the unloading part of the loadunload curve respectively. Then, a set of analytical functions that take the pile-up and sink-in effects into account during instrumented sharp indentation were solved using numerical methods These analytical functions were defined within an identified representative plastic strain, εr, for the Vickers indenter geometry as a strain level that allows for the description of the indentation loading response independent of strain hardening exponent, n.

Nanomechanical Properties of TiO2 Granular Thin Films

Post-deposition annealing effects on nanomechanical properties of granular TiO2 films on soda-lime glass substrates were studied. In particular, the effects of Na diffusion on the films' mechanical properties were examined. TiO2 photocatalyst films, 330 nm thick, were prepared by dip-coating using a TiO2 sol, and were annealed between 100 °C and 500 °C. Film's morphology, physical and nanomechanical properties were characterized by atomic force microscopy, X-ray photoelectron spectroscopy, X-ray diffraction, differential thermo-gravimetric analysis, and nanoindentation. Contrary to expectations, the maximum film hardness was achieved for 300°C annealing, with a value of 0.69±0.05 GPa. Higher annealing temperatures resulted in inferior mechanical properties. No pile-up or sink-in effects were observed with minimal creep for the 300 °C annealed sample. Considerable decrease in the amount of chemisorbed water was found with increasing annealing temperature, causing gel films densification, explaining the increasing trend of hardness with annealing temperature between 100 °C and 300 °C. DTA/TGA results also confirmed the weight loss and the endothermic reaction due to desorption of chemisorbed water. Decrease in hardness above 300 °C annealing is attributed to thermal diffusion of Na ions from the glass substrate, confirmed by nanoindentation tests on TiO2 films deposited on fused quartz, which did not exhibit hardness decrease after 300 °C annealing.

Nano-mechanical properties of silver-welded YBCO bulks

The mechanical properties of melt-textured YBCO bulk boundaries are a topic of special interest especially in the manufacturing of superconductor devices for engineering applications. Instrumented indentation technique is a powerful tool widely employed to characterize the mechanical properties of small volumes. We presented results of the nanohardness (H) and Young's modulus (E) across [001]-welds fabricated by silver welding. The residual imprints performed by a sharp tip indenter were observed by Field Emission Scanning Electron Microscope (FE-SEM) to investigate the different fracture mechanisms nucleated during the indentation process. Results show a decrease of the nanohardness across the grain boundary related to the appearance of a "welding path" free of Y-211 particles. The FE-SEM images show chipping and sink-in effects in that region. Remarkably, for zero-angle welds the mechanical properties are unaltered across the joint, thus probing the high quality of silver welds for large-scale applications.

A procedure to prevent pile up effects on the analysis of spherical indentation data in elastic–plastic materials

Indentation tests are commonly applied to determine surface mechanical properties of very different kind of materials. In many circumstances, results provided by indentation are different to those obtain by more traditional tests (tensile, compression, etc.). In the particular case of elastic–plastic solids, phenomena like pile up or sink in cause deviations in Young’s modulus and hardness data if any correction procedure is applied to the experimental load–displacement curves. In this work, a finite element model was used to evaluate the pile up and sink in effects on the determination of mechanical properties in a wide range of elastic–plastic materials. Several combinations of Young’s modulus, yield stress and hardening exponent were considered. Taking into account the non-geometrical similarity of spherical tips, this configuration was chosen to suggest a new procedure, based on a combination of results obtained from tests performed at multiple maximum loads. The method gives consistent results and it was experimentally validated comparing nano-indentation and tensile tests of bulk metallic materials.

Comparison between conventional Vickers hardness and indentation hardness obtained with different instruments

Abstract An extensive comparison between the conventional Vickers hardness at 500 mN and indentation hardness measured with Vickers indenters at 500 mN is presented for up to 20 different eaterials and for three different instruments. Additionally, the indentation modulus is compared to Young's modulus, which was measured with alternative methods or taken from the literature. It is shown that the agreement betweef the results from depth-sensing indentation and the reference values can be improved by additional corrections, for the calculation of the indentation area. With corrections the mean hardness difference to the Vickers hardness reference as average of all investigated materaals can be reduced to about 10% although disturbing pile-up or sink-in effects can still not be considered. For the modulus, the mean difference was only about 6%.

Analysis of sharp-tip-indentation load–depth curve for contact area determination taking into account pile-up and sink-in effects

Hardness and elastic modulus of micromaterials can be evaluated by analyzing instrumented sharp-tip-indentation load–depth curves. The present study quantified the effects of tip-blunting and pile-up or sink-in on the contact area by analyzing indentation curves. Finite-element simulation and theoretical modeling were used to describe the detailed contact morphologies. The ratio f of contact depth, i.e., the depth including elastic deflection and pile-up and sink-in, to maximum indentation depth, i.e., the depth measured only by depth sensing, ignoring elastic deflection and pile-up and sink-in, was proposed as a key indentation parameter in evaluating real contact depth during indentation. This ratio can be determined strictly in terms of indentation-curve parameters, such as loading and unloading slopes at maximum depth and the ratio of elastic indentation energy to total indentation energy. In addition, the value of f was found to be independent of indentation depth, and furthermore the real contact area can be determined and hardness and elastic modulus can be evaluated from f. This curve-analysis method was verified in finite-element simulations and nanoindentation experiments.

Indentation Curve Analysis for Pile-up, Sink-in and Tip-Blunting Effects in Sharp Indentations

ABSTRACTHardness and elastic modulus can be derived from instrumented sharp indentation curves by considering the effects of materials pile-up and sink-in and tip blunting. In particular, this study quantifies pile-up or sink-in effects in determining contact area based on indentation-curve analysis. Two approaches, finite-element simulation and theoretical modeling, were used to describe the detailed contact morphologies. The ratio of contact depth to maximum indentation depth was proposed as a key indentation parameter and was found to be a material constant independent of indentation load. In addition, this parameter can be determined strictly in terms of indentation-curve parameters, such as loading and unloading slopes at maximum depth and indentation energy ratio. This curve-analysis method was verified by finite-element simulations and nanoindentation experiments.

Indentation plastic displacement field: Part II. The case of hard films on soft substrates

The plastic displacements around Knoop indentations made in hard titanium/aluminum multilayered films on soft aluminum alloy substrates have been studied. Indentations were cross-sectioned and imaged using focused-ion-beam (FIB) milling and high-resolution scanning electron microscopy (SEM), respectively. The FIB milling method has the advantage of removing material in a localized region without producing mechanical damage to the specimen. The micrographs of the cross-sectioned indentations indicate that most of the plastic deformation around the indentation is dominated by the soft aluminum substrate. There is a very small change in the multilayered film thickness around the indentation—less than 10%. The plastic deformation of the thin film resembles a membrane being deflected by a localized pressure gradient across the membrane. Stress-induced voids are also observed in the multilayered film, especially in the area around the indentation apex. The density and the size of the voids increase with indentation depth. Indentation sink-in effects are observed in all of the indentations inspected. Based on the experimental results, the amount of sink-in of the hard film–soft substrate composite is larger than the bulk substrate and film alone. This is confirmed by the finite element analyses conducted in this work.