Simplified Area Function for Sharp Indenter Tips in Depth-sensing Indentation

2002 ◽  
Vol 17 (5) ◽  
pp. 1143-1146 ◽  
Author(s):  
Jeremy Thurn ◽  
Robert F. Cook
Keyword(s):  
Cone Angle ◽  
Indentation Load ◽  
Depth Sensing ◽  
Area Function ◽  
Eden Prairie ◽  
Two Parameters ◽  
Tip Radius ◽  
Hardness Values ◽  
Effective Cone ◽  
Two Parameter

A two-parameter “area function” characterizing the depth-dependent projected area of an indenter was introduced and applied to a Berkovich tip. The two parameters have physical meaning, corresponding to the effective tip radius and effective cone angle. The indenter tip was calibrated on a commercial load-controlled Nano Indentert® XP (MTS Systems Corp., Eden Prairie, MN). All calibrations were carried out using the procedure of Oliver and Pharr [J. Mater. Res. 7, 1564 (1992)] using several homogeneous materials. Plane-strain modulus and hardness values deconvoluted from indentation load–displacement traces using the calibrated two-parameter area function compared well with the values determined using the empirical eight-parameter area function of Oliver and Pharr.

Depth-sensing indentation at macroscopic dimensions

2002 ◽  
Vol 17 (10) ◽  
pp. 2679-2690 ◽  
Author(s):  
Jeremy Thurn ◽  
Dylan J. Morris ◽  
Robert F. Cook
Keyword(s):  
Contact Area ◽  
Peak Load ◽  
Ceramic Materials ◽  
Depth Sensing ◽  
Macroscopic Scale ◽  
Load Displacement ◽  
Tip Radius ◽  
Hardness Values ◽  
Two Parameter

A macroscopic-scale depth-sensing indentation apparatus with the ability to be mounted on an inverted microscope for in situ observation of contact events was calibrated using the Oliver and Pharr [J. Mater. Res. 7, 1564 (1992)] procedure with a two-parameter area function. The calibrated Vickers tip was used to determine the projected contact area at peak load and the modulus and hardness of a variety of non-metallic materials through deconvolution of the measured load-displacement traces. The predicted contact area was found to be identical to the measured area of residual contact impressions. Furthermore, for transparent ceramic materials the projected contact area during loading was found to be the same as the area measured from the diagonal of post-indentation residual contact impressions. The modulus and hardness values deconvoluted from the load–displacement traces were compared with independent measurements. The effects of sample clamping, column compliance, and tip radius on the load–displacement data and inferred materials properties were also examined. It is suggested that the simplicity of instrumentation and operation, combined with the ability to observe indentations optically, even in situ, makes macroscopic-scale depth-sensing indentation ideal for fundamental studies of contact mechanics.

Nanoindentation Hardness Tests Using a Point Contact Microscope

1994 ◽  
Vol 116 (1) ◽  
pp. 175-180 ◽  
Author(s):  
C. J. Lu ◽  
D. Bogy ◽  
R. Kaneko
Keyword(s):  
Point Contact ◽  
Indentation Load ◽  
Apex Angle ◽  
Indentation Force ◽  
Single Leaf ◽  
Leaf Springs ◽  
Hardness Tests ◽  
Nanoindentation Hardness ◽  
Tip Radius ◽  
Hardness Values

The Point Contact Microscope (PCM), developed in NTT’s Kaneko Research Laboratory, is used to conduct hardness tests on polycarbonate and gold at indentation depths in the range of about 5-100 nm. Different diamond indenters, which are attached to single leaf springs of various stiffnesses, are used to study the effects of tip radius and apex angle on the measured hardness values. The indentation depth versus force and hardness versus force relations for various tip conditions are examined. It is found that the hardness value obtained increases for small values of indentation load and approaches a tip-independent value for larger loads. The hardness is sensitive to the indentation force and tip radius in the limit of small indentation depths. In this case, a standard indenter and a fixed load should be used to compare the hardnesses of different materials. The effect of the apex angle on the hardness is relatively insignificant.

Indentation Testing of MoSi2

2005 ◽  
Vol 290 ◽  
pp. 288-291 ◽  
Author(s):  
M. Henžel ◽  
Peter Zimovčák ◽  
Ján Dusza ◽  
András Juhász ◽  
Janos Lendvai
Keyword(s):  
High Temperature ◽  
Indentation Load ◽  
High Temperature Deformation ◽  
Temperature Deformation ◽  
Slip Systems ◽  
Deformation Characteristics ◽  
Depth Sensing ◽  
Indentation Methods ◽  
Load Size ◽  
Hardness Values

Indentation methods have been used for the study of the hardness and deformation characteristics MoSi2. Micro-nanoindentation tests at loads from 10 mN to 2000 mN were carried out using the depth-sensing method. Measurements of the microhardness using conventional Vickers method was carried out at loads of 500 mN, 1000 mN and 2000 mN. The Universal (Martens), Plastic and conventional Vickers hardness values were calculated at different indentation loads. Evident indentation load - size effect was found in both materials. According to the results, the pre-strain reduces the micro-nano hardness values, probably due to the activation of slip systems during the high-temperature deformation.

Micro-Hardness and Morphology of LDPE Influenced by Beta Radiation

2014 ◽  
Vol 606 ◽  
pp. 253-256 ◽  
Author(s):  
Martin Ovsik ◽  
Petr Kratky ◽  
David Manas ◽  
Miroslav Manas ◽  
Michal Stanek ◽  
...  
Keyword(s):  
Mechanical Properties ◽  
Hardness Test ◽  
Polymer Materials ◽  
Beta Radiation ◽  
Micro Hardness ◽  
X Ray Diffraction ◽  
Depth Sensing ◽  
Surface Layers ◽  
Hardness Values ◽  
Different Doses

This article deals with the influence of different doses of Beta radiation to the structure and mico-mechanical properties of Low-density polyethylene (LDPE). Hard surface layers of polymer materials, especially LDPE, can be formed by radiation cross-linking by β radiation with doses of 33, 66 and 99 kGy. Material properties created by β radiation are measured by micro-hardness test using the DSI method (Depth Sensing Indentation). Individual radiation doses caused structural and micro-mechanical changes which have a significant effect on the final properties of the LDPE tested. The highest values of micro-mechanical properties were reached at radiation dose of 66 and 99 kGy, when the micro-hardness values increased by about 21%. The changes were examined and confirmed by X-ray diffraction.

scholarly journals Application of the plasticity characteristic determined by the indentation technique for evaluation of mechanical properties of coatings: I. specific features of the test method procedure

2004 ◽  
Vol 36 (1) ◽  
pp. 27-41 ◽  
Author(s):  
A.V. Byakova ◽  
Yu.V. Milman ◽  
A.A. Vlasov
Keyword(s):  
Mechanical Properties ◽  
Indentation Load ◽  
Test Method ◽  
Simplified Model ◽  
Micro Hardness ◽  
Properties Of Coatings ◽  
Modified Model ◽  
Plasticity Characteristic ◽  
Measurement Results ◽  
Hardness Values

Specific features of the test method procedure capable for determining the plasticity characteristic dH by indentation of inhomogeneous coatings affected by residual stress was clarified. When the value of the plasticity characteristic for coating was found to be as great as dH > 0.5 a simplified model was found to be reasonably adequate, while a modified model assumed compressibility of the deformation core beneath indentation. The advantage of the modified approach compared to the simplified one was grounded experimentally only if the elastic deformation for coating becomes greater than ?e ? 3.5%, resulting in the decrease of plasticity characteristic dH < 0.5. To overcome non accuracy caused by the effect of the scale factor on measurement results a comparison of different coatings was suggested using stabilized values of the plasticity characteristic dH determined under loads higher than critical, P ? Pc, ensuring week dependence of micro hardness values on the indentation load.

Two parameters are required for a Budyko function to describe the land-atmosphere interaction

2021 ◽  
Author(s):  
Daeha Kim ◽  
Jong Ahn Chun
Keyword(s):  
Land Surface ◽  
River Basins ◽  
Control Surface ◽  
Primary Control ◽  
Evaporative Demand ◽  
Atmosphere Interaction ◽  
The Mean ◽  
Two Parameters ◽  
Two Parameter ◽  
Surface Changes

&lt;p&gt;While the Budyko framework has been a simple and convenient tool to assess runoff (Q) responses to climatic and surface changes, it has been unclear how parameters of a Budyko function represent the vertical land-atmosphere interactions. Here, we explicitly derived a two-parameter equation by correcting a boundary condition of the Budyko hypothesis. The correction enabled for the Budyko function to reflect the evaporative demand (E&lt;sub&gt;p&lt;/sub&gt;) that actively responds to soil moisture deficiency. The derived two-parameter function suggests that four physical variables control surface runoff; namely, precipitation (P), potential evaporation (E&lt;sub&gt;p&lt;/sub&gt;), wet-environment evaporation (E&lt;sub&gt;w&lt;/sub&gt;), and the catchment properties (n). We linked the derived Budyko function to a definitive complementary evaporation principle, and assessed the relative elasticities of Q to climatic and land surface changes. Results showed that P is the primary control of runoff changes in most of river basins across the world, but its importance declined with climatological aridity. In arid river basins, the catchment properties play a major role in changing runoff, while changes in E&lt;sub&gt;p&lt;/sub&gt; and E&lt;sub&gt;w&lt;/sub&gt; seem to exert minor influences on Q changes. It was also found that the two-parameter Budyko function can capture unusual negative correlation between the mean annual Q and E&lt;sub&gt;p&lt;/sub&gt;. This work suggests that at least two parameters are required for a Budyko function to properly describe the vertical interactions between the land and the atmosphere.&lt;/p&gt;

A pragmatic approach for the evaluation of depth-sensing indentation in the self-similar regime

2021 ◽  
pp. 1-24
Author(s):  
Hamidreza Mahdavi ◽  
Konstantinos Poulios ◽  
Christian F. Niordson
Keyword(s):  
Finite Element ◽  
Element Model ◽  
Depth Sensing ◽  
Finite Element Software ◽  
Element Simulation ◽  
Unique Material ◽  
Reverse Analysis ◽  
Supplementary Material ◽  
Two Parameters ◽  
Force Displacement

Abstract This work evaluates and revisits elements from the depth-sensing indentation literature by means of carefully chosen practical indentation cases, simulated numerically and compared to experiments. The aim is to close a series of debated subjects, which constitute major sources of inaccuracies in the evaluation of depth-sensing indentation data in practice. Firstly, own examples and references from the literature are presented in order to demonstrate how crucial self-similarity detection and blunting distance compensation are, for establishing a rigorous link between experiments and simple sharp-indenter models. Moreover, it is demonstrated, once again, in terms of clear and practical examples, that no more than two parameters are necessary to achieve an excellent match between a sharp indenter finite element simulation and experimental force-displacement data. The clear conclusion is that reverse analysis methods promising to deliver a set of three unique material parameters from depth-sensing indentation cannot be reliable. Lastly, in light of the broad availability of modern finite element software, we also suggest to avoid the rigid indenter approximation, as it is shown to lead to unnecessary inaccuracies. All conclusions from the critical literature review performed lead to a new semi-analytical reverse analysis method, based on available dimensionless functions from the literature and a calibration against case specific finite element simulations. Implementations of the finite element model employed are released as supplementary material, for two major finite element software packages.

The determination of film hardness from the composite response of film and substrate to nanometer scale indentations

1992 ◽  
Vol 7 (11) ◽  
pp. 3056-3064 ◽  
Author(s):  
B.D. Fabes ◽  
W.C. Oliver ◽  
R.A. McKee ◽  
F.J. Walker
Keyword(s):  
Finite Element ◽  
Film Thickness ◽  
Weighted Average ◽  
Element Model ◽  
Basic Structure ◽  
Depth Sensing ◽  
Area Function ◽  
Volume Fractions ◽  
Film Hardness ◽  
Titanium Coatings

Two equations for determining the hardness of thin films from depth-sensing indentation data are examined. The first equation is based on an empirical fit of hardness versus indenter displacement data obtained from finite element calculations on a variety of hypothetical films. The second equation is based on a model which assumes that measured hardness is determined by the weighted average of the volume of plastically deformed material in the coating and that in the substrate. The equations are evaluated by fitting the predicted hardness versus contact depth to data obtained from titanium coatings on a sapphire substrate. Only the volume fractions model allows the data to be fitted with a single adjustable parameter, the film hardness; the finite element equation requires two thickness-dependent parameters to obtain acceptable fits. It is argued that the difficulty in applying the finite element model lies in the use of an unrealistic area function for the indenter. For real indenters, which have finite radii, the area function must appear explicitly in the final equation. This is difficult to do with the finite element approach, but is naturally incorporated into the volume fractions equation. Finally, using the volume fractions approach the hardnesses of the titanium films are found to be relatively insensitive to film thickness. Thus, the apparent increase in hardness with decreasing film thickness for the titanium films is most likely due to increased interactions between the film and substrate for the thinner films rather than to a change in the basic structure of the titanium films.

Effect of heat treatment on elastic properties of separated thermal barrier coatings

1999 ◽  
Vol 14 (12) ◽  
pp. 4643-4650 ◽  
Author(s):  
D. Basu ◽  
C. Funke ◽  
R. W. Steinbrech
Keyword(s):  
Elastic Moduli ◽  
Bulk Material ◽  
Mercury Porosimetry ◽  
Indentation Load ◽  
Elastic Response ◽  
Depth Sensing ◽  
Heat Treated ◽  
Data Points ◽  
Plasma Sprayed ◽  
High Degree

Elastic response behavior of four different plasma-sprayed deposits has been investigated using depth-sensing micro-indentation technique. Due to the high degree of porosity and inhomogeneity of the coatings, the characteristic elastic moduli were found to be in the range of 20–75% of that of the dense bulk material (200 GPa). Considering the wide variation of properties, 150 data points were generated with five different indentation loads for each coating, and statistical tools were employed to represent the scatter of the data. The characteristic elastic moduli of all the coatings were observed to be almost doubled when the magnitude of indentation load was reduced from the highest (1000 mN) to the lowest (30 mN). The coatings were subsequently heat treated at 1100 °C, the operational temperature of a gas turbine, for 2, 25, and 100 h, and in all the coating grades the corresponding elastic moduli increased significantly. However, the stiffening effect was not uniform in two grades and was more pronounced for the smaller indentation loads. The increase in elastic modulus is attributed to elimination of fine porosity and sintering neck formation, an assumption also supported by the results of mercury porosimetry.

The influence of oxide and adsorbates on the nanomechanical response of silicon surfaces

2000 ◽  
Vol 15 (2) ◽  
pp. 546-553 ◽  
Author(s):  
S. A. Syed Asif ◽  
K. J. Wahl ◽  
R. J. Colton
Keyword(s):  
Oxide Layer ◽  
Mechanical Response ◽  
Surface Preparation ◽  
Oxide Thickness ◽  
Silicon Surfaces ◽  
Depth Sensing ◽  
Hydrophilic Surfaces ◽  
Surface Oxides ◽  
Tip Radius ◽  
Substrate Influence

In this article we report the influence of surface oxides and relative humidity on the nanomechanical response of hydrophobic and hydrophilic Si surfaces. Depth-sensing nanoindentation combined with force modulation enabled measurement of surface forces, surface energy, and interaction stiffness prior to contact. Several regimes of contact were investigated: pre-contact, apparent contact, elastic contact, and elasto-plastic contact. Both humidity and surface preparation influenced the surface mechanical properties in the pre- and apparent-contact regimes. Meniscus formation was observed for both hydrophobic and hydrophilic surfaces at high humidity. Influence of humidity was much less pronounced on hydrophobic surfaces and was fully reversible. In the elastic and elasto-plastic regimes, the mechanical response was dependent on oxide layer thickness. Irreversibility at small loads (300 nN) was due to the deformation of the surface oxide. Above 1 μN, the deformation was elastic until the mean contact pressure reached 11 GPa, whereby Si underwent a pressure-induced phase transformation resulting in oxide layer pop-in and breakthrough. The critical load required for pop-in was dependent on oxide thickness and tip radius. For thicker oxide layers, substrate influence was reduced and plastic deformation occurred within the oxide film itself without pop-in. Elastic modulus and hardness of both the oxide layer and Si substrate were measured quantitatively for depths <5 nm.

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