On the Indentation Modulus of Sintered Materials

2013 ◽  
Vol 586 ◽  
pp. 190-193
Author(s):  
Miriam Kupková ◽  
Martin Kupka
Keyword(s):  
Experimental Data ◽  
Indentation Size Effect ◽  
Displacement Curve ◽  
Indentation Modulus ◽  
Indentation Size ◽  
Depth Sensing ◽  
Nano Indentation ◽  
Individual Grains ◽  
Theoretical Results ◽  
Sintered Materials

When the depth-sensing (nano)indentation is applied to sintered samples, measured properties, which are expected to represent the material of an individual grain, seem to depend on the overall porosity of the macroscopic sample. To understand such a result, it is assumed that while the nanoindenter penetrates into the surface grain and probes the properties of its material, the grain itself serves as another, larger indenter indenting the rest of sample and probing the properties that represent the bulk of material rather than individual grains. Load vs. displacement curve reflects the synergetic response of these two “indenters” and so it contains information about the sample’s mechanical properties at both microscopic and macroscopic scales. Obtained theoretical results agree qualitatively with the experimental data (the dependence of the indentation modulus on the porosity of sample; the indentation size effect).

The use of nanoindentation for determining internal lengths and the constitutive response of monument materials: models and experiments

2016 ◽  
Vol 25 (1-2) ◽  
pp. 57-60 ◽  
Author(s):  
Avraam A. Konstantinidis ◽  
George Frantziskonis ◽  
Harm Askes ◽  
Elias C. Aifantis
Keyword(s):  
Experimental Data ◽  
Size Effect ◽  
Indentation Size Effect ◽  
Gradient Elasticity ◽  
Alternative Interpretation ◽  
Indentation Size ◽  
Elasticity Equation ◽  
Constitutive Response

AbstractAn alternative interpretation of nanoindentation experimental data and the associated phenomenon of indentation size effect (ISE) is proposed on the basis of a simple gradient elasticity equation, used to account for the development of elastic gradients generated by the geometry characterizing the indenter-specimen system. An application is considered for marble, i.e. a construction/restoration material.

scholarly journals Atomic force microscopy study of nanoindentation deformation and indentation size effect in MgO crystals

1999 ◽  
Vol 14 (10) ◽  
pp. 3973-3982 ◽  
Author(s):  
K. Sangwal ◽  
P. Gorostiza ◽  
J. Servat ◽  
F. Sanz
Keyword(s):  
Experimental Data ◽  
Plastic Deformation ◽  
Atomic Force Microscopy ◽  
Size Effect ◽  
Deformation Zone ◽  
Indentation Size Effect ◽  
Indentation Size ◽  
Depth Of Penetration ◽  
Force Microscopy ◽  
Atomic Force

The dependences of various nanoindentation parameters, such as depth of penetration d, indentation diameter a, deformation zone radius R, and height h of hills piled up around indents, on applied load were investigated for the initial (unrecovered) stage of indentation of the (100) cleavage faces of MgO crystals by square pyramidal Si tips for loads up to 10 μN using atomic force microscopy. The experimental data are analyzed using theories of elastic and plastic deformation. The results revealed that (i) a, R, and h linearly increase with d; (ii) the development of indentation size and deformation zone and the formation of hills are two different processes; (iii) the load dependence of nanohardness shows the normal indentation size effect (i.e., the hardness increases with a decrease in load); and (iv) there is an absence of plastic deformation involving the formation of slip lines around the indentations. It is found that Johnson's cavity model of elastic–plastic boundary satisfactorily explains the experimental data. The formation of hills around indentations is also consistent with a new model (i.e., indentation crater model) based on the concept of piling up of material of indentation cavity as hills.

Indentation size effects in polymers and related rotation gradients

2007 ◽  
Vol 22 (6) ◽  
pp. 1662-1672 ◽  
Author(s):  
Chung-Souk Han ◽  
Svetoslav Nikolov
Keyword(s):  
Experimental Data ◽  
Size Effects ◽  
Indentation Size Effect ◽  
Polymer Chains ◽  
Indentation Size ◽  
Proposed Model ◽  
Dislocation Densities ◽  
Model Size ◽  
Depth Ranges ◽  
Plastic Extension

Similar to metals, the hardness of many polymers increases with decreasing indentation depths at depth ranges from several microns down to several nanometers. While for metals such phenomena are commonly attributed to geometrically necessary dislocation densities, such an explanation cannot be applied to polymers. To provide a micromechanically motivated model for the indentation size effect in polymers, here we propose an elasto-plastic extension of the higher order elasticity model recently developed by the authors. In this model, size effects in polymers (as well as in nematic liquid crystals) are related to Frank elasticity arising from bending distortions of the polymer chains and their interactions. On the basis of this theory, we derive a simple model for indentation size effects in polymers. Unlike other models, our model includes only elastic size effects due to rotational gradients. It is shown that the proposed model can explain the experimentally observed size effects in polymers. Together with the existing experimental data mentioned here, new experimental data for silicon rubber are also presented and discussed.

MECHANICAL PROPERTIES OF FERROELECTRIC CERAMIC NANOCOMPOSITES

2005 ◽  
Vol 04 (04) ◽  
pp. 607-613
Author(s):  
KWOK LUN LEE ◽  
AI KAH SOH ◽  
XIAO XING WANG ◽  
KIN WING KWOK
Keyword(s):  
Mechanical Properties ◽  
Indentation Size Effect ◽  
Ferroelectric Ceramic ◽  
Nano Particles ◽  
Compression Tests ◽  
Indentation Size ◽  
Depth Sensing ◽  
Reduced Modulus ◽  
Hardness Values ◽  
True Hardness

The micro- and nano-indentation techniques and compression tests were employed to determine the mechanical properties of PZT based composites dispersed with Al 2 O 3 nano-particles for comparison. Compared with the reduced modulus, the nano-hardness, which exhibited indentation size effect (ISE), seemed to be more sensitive to the indentation depth. The true hardness values were deduced, based on the modified proportional specimen resistance (PSR) model, from the depth sensing machine and micro-indenter. Both the micro- and nano-hardness of the nano-composites confirmed that the hardness was best improved by addition of 0.5wt% of Al 2 O 3.

Non-direct estimations of adhesive and elastic properties of materials by depth-sensing indentation

2008 ◽  
Vol 464 (2098) ◽  
pp. 2759-2776 ◽  
Author(s):  
Feodor M Borodich ◽  
Boris A Galanov
Keyword(s):  
Experimental Data ◽  
Elastic Properties ◽  
Measurement Errors ◽  
Direct Determination ◽  
Adhesive Contact ◽  
Work Of Adhesion ◽  
Displacement Curve ◽  
Depth Sensing ◽  
Adhesive Properties ◽  
Force Displacement

Using the connection between depth-sensing indentation by spherical indenters and mechanics of adhesive contact, a new method for non-direct determination of adhesive and elastic properties of contacting materials is proposed. At low loads, the force–displacement curves reflect not only elastic properties but also adhesive properties of the contact, and therefore one can try to extract from experiments both the elastic characteristics of contacting materials (such as the reduced elastic modulus) and characteristics of molecular adhesion (such as the work of adhesion and the pull-off force) using a non-direct approach. The direct methods of estimations of the adhesive characteristics of materials currently used in experiments are rather complicated due to the instability of the experimental force–displacement diagrams for ultra-low tensile forces. The proposed method is based on the use of the stable experimental data for the elastic stage of the force–displacement curve and the mechanics of adhesive contact for spherical indenters. Since the experimental data always have some measurement errors, mathematical techniques for solving ill-posed problems are employed.

A dislocation-based yield strength model for nano-indentation size effect

2021 ◽  
pp. 146442072199279
Author(s):  
Ping Tao ◽  
Fei Ye ◽  
Jianming Gong ◽  
Richard A Barrett ◽  
Seán B Leen
Keyword(s):  
Finite Element ◽  
Yield Strength ◽  
Size Effect ◽  
Finite Element Modelling ◽  
Indentation Size Effect ◽  
Dual Phase ◽  
Strength Model ◽  
Indentation Size ◽  
Element Modelling ◽  
Nano Indentation

This paper presents a dislocation-based yield strength model for the nano-indentation size effect. The model is based on functional expressions involving the densities of statistically stored dislocations and geometrically necessary dislocations. A single-phase austenitic stainless steel (316L) and a ferrite-austenite dual-phase steel (2205) are used here as the case-study materials to validate the proposed model. Experimental testing and finite element modelling of nano-indentation of the two materials are presented. Experimental tests are performed in the indentation load range from 1000[Formula: see text] to 10000[Formula: see text]. For 2205 steel, finite element modelling is performed using a dual-phase microstructure-based model. It is shown that, with consideration of statistically stored dislocations and geometrically necessary dislocations, finite element modelling results can reproduce measured load–displacement curves and hence, the size effect, within an error range of about 5%.

Analysis of Indentation Size Effect of Vickers Hardness Tests of Steels

2013 ◽  
Vol 652-654 ◽  
pp. 1307-1310 ◽  
Author(s):  
Nyoman Budiarsa ◽  
Andrew Norbury ◽  
Xiao Xiang Su ◽  
Gareth Bradley ◽  
Xue Jun Ren
Keyword(s):  
Experimental Data ◽  
Size Effect ◽  
Power Law ◽  
Vickers Hardness ◽  
Material Properties ◽  
Indentation Size Effect ◽  
Indentation Load ◽  
Indentation Size ◽  
Load Range ◽  
Hardness Tests

In this work, the indentation size effect (ISE) in Vickers hardness tests of steel with selected heat treatments (annealed or tempered) has been investigated and analysed. Systematical hardness tests were performed within a commonly used micro-load range. The experimental data was analysed according to the Meyer power-law and the proportional specimen resistance (PSR) models and the link between ISE and material properties was discussed. The results showed that the experimental data fitted well with the Mayers power-law (P = A.dn) and the PSR (P/d = al + a2d) models. The ISE index (n) showed a good correlation with the hardness-elastic modulus ratio (H/E), which potentially could be used to predict the relative contributions of the elastic and plastic deformation contact area under indentation load and to normalize the hardness values for inverse material properties .

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