On the generality of the relationship among contact stiffness, contact area, and elastic modulus during indentation

1992 ◽  
Vol 7 (3) ◽  
pp. 613-617 ◽  
Author(s):  
G.M. Pharr ◽  
W.C. Oliver ◽  
F.R. Brotzen
Keyword(s):  
Elastic Modulus ◽  
Contact Area ◽  
Contact Stiffness ◽  
Elastic Half Space ◽  
Elastic Contact ◽  
Simple Relationship ◽  
Depth Sensing ◽  
Force Microscopy ◽  
Atomic Force ◽  
The Relationship

Results of Sneddon's analysis for the elastic contact between a rigid, axisymmetric punch and an elastic half space are used to show that a simple relationship exists among the contact stiffness, the contact area, and the elastic modulus that is not dependent on the geometry of the punch. The generality of the relationship has important implications for the measurement of mechanical properties using load and depth sensing indentation techniques and in the measurement of small contact areas such as those encountered in atomic force microscopy.

Effect of Pile-Up on the Mechanical Characteristics of Steel by Depth Sensing Indentation

2014 ◽  
Vol 606 ◽  
pp. 81-84 ◽  
Author(s):  
Peter Burik ◽  
Ladislav Pešek ◽  
Lukáš Voleský
Keyword(s):  
Contact Area ◽  
Mechanical Characteristics ◽  
Micromechanical Model ◽  
Indentation Load ◽  
Elastic Contact ◽  
Depth Sensing ◽  
Force Microscopy ◽  
Atomic Force ◽  
Pile Up ◽  
Load Displacement

Mechanical properties by depth sensing indentation are derived from the indentation load-displacement data used a micromechanical model developed by Oliver & Pharr (O&P). However, O&P analysis on the indentation unloading curve is developed from a purely elastic contact mechanics (sink-in). The applicability of O&P analysis is limited by the materials pile-up. However, when it does, the contact area is larger than that predicted by elastic contact theory (material sinks-in during purely elastic contact), and both hardness H and Youngs modulus E are overestimated, because their evaluation depends on the contact area deduced from the load-displacement data. H can be overestimated by up to 60 % and E by up to 30 % depending on the extent of pile-up [1,2]. It is therefore important to determine the effect of pile-up on obtained mechanical characteristics of the material by depth sensing indentation. The work experimentally analyses the effect of pile-up height on mechanical characteristics H and E, which are determined by O&P analysis. Pile-up height was measured by atomic force microscopy (AFM).

scholarly journals Depth-Sensing Hardness Measurements to Probe Hardening Behaviour and Dynamic Strain Ageing Effects of Iron during Tensile Pre-Deformation

Nanomaterials ◽  
2020 ◽  
Vol 11 (1) ◽  
pp. 71
Author(s):  
Lyubomira Veleva ◽  
Peter Hähner ◽  
Andrii Dubinko ◽  
Tymofii Khvan ◽  
Dmitry Terentyev ◽  
...  
Keyword(s):  
Elastic Modulus ◽  
Room Temperature ◽  
Dynamic Strain ◽  
Test Results ◽  
Dynamic Strain Ageing ◽  
Depth Sensing ◽  
Strain Ageing ◽  
Force Microscopy ◽  
Atomic Force ◽  
Pile Up

This work reports results from quasi-static nanoindentation measurements of iron, in the un-strained state and subjected to 15% tensile pre-straining at room temperature, 125 °C and 300 °C, in order to extract room temperature hardness and elastic modulus as a function of indentation depth. The material is found to exhibit increased disposition for pile-up formation due to the pre-straining, affecting the evaluation of the mechanical properties of the material. Nanoindentation data obtained with and without pre-straining are compared with bulk tensile properties derived from the tensile pre-straining tests at various temperatures. A significant mismatch between the hardness of the material and the tensile test results is observed and attributed to increased pile-up behaviour of the material after pre-straining, as evidenced by atomic force microscopy. The observations can be quantitatively reconciled by an elastic modulus correction applied to the nanoindentation data, and the remaining discrepancies explained by taking into account that strain hardening behaviour and nano-hardness results are closely affected by dynamic strain ageing caused by carbon interstitial impurities, which is clearly manifested at the intermediate temperature of 125 °C.

Pile-Up Correction of Mechanical Characteristics of Individual Phases in Various Steel by Depth Sensing Indentation

2015 ◽  
Vol 662 ◽  
pp. 7-10 ◽  
Author(s):  
Peter Burik ◽  
Ladislav Pešek ◽  
Lukáš Voleský
Keyword(s):  
Atomic Force Microscopy ◽  
Elastic Modulus ◽  
Grain Boundaries ◽  
Mechanical Characteristics ◽  
Depth Sensing ◽  
The Real ◽  
Force Microscopy ◽  
Atomic Force ◽  
Pile Up ◽  
Shape And Size

The Oliver–Pharr method has extensively been adopted for measuring hardness and elastic modulus by indentation techniques. However, the method assumes that the contact periphery sinks in, which limits the applicability to the materials pile-up [1]. This study proposes an improved methodology to calculate the real mechanical characteristics of individual phases in various steels with significant pile-up. Pile-up correction of mechanical characteristics is based on ratio of pile-up height and contact depth. Pile-up height was measured by atomic force microscopy (AFM). The effect of grain boundaries on the shape and size of the pile-up lobes was also discussed.

Correction factor for contact area in nanoindentation measurements

2005 ◽  
Vol 20 (3) ◽  
pp. 610-617 ◽  
Author(s):  
Michel Troyon ◽  
Liye Huang
Keyword(s):  
Elastic Modulus ◽  
Correction Factor ◽  
Contact Area ◽  
Basic Equation ◽  
Elastic Moduli ◽  
Contact Stiffness ◽  
Factor Α ◽  
Tip Radius ◽  
The Relationship ◽  
Indenter Shape

In the relationship between unloading contact stiffness, elastic modulus, and contact area, which is the fundamental basic equation for nanoindentation analysis, a multiplicative correction factor is generally needed. Sometimes this correction factor is called γ to take into account the elastic radial inward displacements, and sometimes it is called β to correct for the fact that the indenter shape is not a perfect cone. In reality, these two effects simultaneously coexist and thus it is proposed that this correction factor is α = βγ. From nanoindentation data measured on three materials of different elastic moduli with a sharp Berkovich indenter and a worn one, the tip of which was blunt, it is demonstrated that the correction factor α does not have a constant value for a given material and indenter type but depends on the indenter tip rounding and also on the deformation of the indenter during indentation. It seems that α increases with the tip radius and also with the elastic modulus of the measured materials.

scholarly journals A Universal Model for the Log-Normal Distribution of Elasticity in Polymeric Gels and Its Relevance to Mechanical Signature of Biological Tissues

Biology ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 64
Author(s):  
Arnaud Millet
Keyword(s):  
Elastic Modulus ◽  
Normal Distribution ◽  
Biological Tissues ◽  
Force Microscopy ◽  
Polymeric Gels ◽  
Atomic Force ◽  
Clear Explanation ◽  
Log Normal ◽  
Log Normal Distribution

The mechanosensitivity of cells has recently been identified as a process that could greatly influence a cell’s fate. To understand the interaction between cells and their surrounding extracellular matrix, the characterization of the mechanical properties of natural polymeric gels is needed. Atomic force microscopy (AFM) is one of the leading tools used to characterize mechanically biological tissues. It appears that the elasticity (elastic modulus) values obtained by AFM presents a log-normal distribution. Despite its ubiquity, the log-normal distribution concerning the elastic modulus of biological tissues does not have a clear explanation. In this paper, we propose a physical mechanism based on the weak universality of critical exponents in the percolation process leading to gelation. Following this, we discuss the relevance of this model for mechanical signatures of biological tissues.

Preparation and Research on the Lateral Elastic Modulus of the MnO2 Nanowires

2013 ◽  
Vol 662 ◽  
pp. 84-87
Author(s):  
Yong Jiang ◽  
Jian Cheng Deng ◽  
Yan Huai Ding ◽  
Jiu Ren Yin ◽  
Ping Zhang
Keyword(s):  
Elastic Modulus ◽  
Crystal Form ◽  
Bending Test ◽  
X Ray Diffraction ◽  
Nanowire Diameter ◽  
X Ray ◽  
Three Point Bending ◽  
Force Microscopy ◽  
Atomic Force ◽  
Mno2 Nanowires

MnO2 nanowires with large aspect ratio were successfully synthesized via a hydrothermal method. In this method, Mn(NO3)2 was as a source of manganese and NH4NO3 as an oxidant. The structure and morphology of the MnO2 nanowires were characterized by X ray diffraction (XRD) and scanning electron microscope (SEM). Their lateral elastic modulus was characterized via a nanoscale three-point bending test by atomic force microscopy (AFM) equipped with picoforce. The results indicate that the crystal form of MnO2 was β-MnO2. The elastic modulus of the nanowires decreased with the increase in nanowire diameter. This elastic modulus was in the range of 33.36-77.84GPa as the diameter ranged from 240 to 185nm.

Elastic Modulus of Single Cellulose Microfibrils from Tunicate Measured by Atomic Force Microscopy

2009 ◽  
Vol 10 (9) ◽  
pp. 2571-2576 ◽  
Author(s):  
Shinichiro Iwamoto ◽  
Weihua Kai ◽  
Akira Isogai ◽  
Tadahisa Iwata
Keyword(s):  
Atomic Force Microscopy ◽  
Elastic Modulus ◽  
Cellulose Microfibrils ◽  
Force Microscopy ◽  
Atomic Force

Quantitative mechanical analysis of indentations on layered, soft elastic materials

Soft Matter ◽  
2019 ◽  
Vol 15 (8) ◽  
pp. 1776-1784 ◽  
Author(s):  
Bryant L. Doss ◽  
Kiarash Rahmani Eliato ◽  
Keng-hui Lin ◽  
Robert Ros
Keyword(s):  
Atomic Force Microscopy ◽  
Elastic Modulus ◽  
Cell Mechanics ◽  
Biological Samples ◽  
Mechanical Analysis ◽  
Elastic Materials ◽  
Mechanical Heterogeneity ◽  
Popular Method ◽  
Force Microscopy ◽  
Atomic Force

Atomic force microscopy (AFM) is becoming an increasingly popular method for studying cell mechanics, however the existing analysis tools for determining the elastic modulus from indentation experiments are unable to quantitatively account for mechanical heterogeneity commonly found in biological samples.

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