Analysis of nanoindentation load-displacement loading curves

1996 ◽  
Vol 11 (8) ◽  
pp. 1987-1995 ◽  
Author(s):  
S. V. Hainsworth ◽  
H. W. Chandler ◽  
T. F. Page
Keyword(s):  
Young’S Modulus ◽  
Young's Modulus ◽  
Elastic Recovery ◽  
Hard Coatings ◽  
Attractive Alternative ◽  
Indentation Hardness ◽  
Test Volume ◽  
Considerable Difficulty ◽  
Load Displacement ◽  
The Relationship

Nanoindentation load-displacement curves provide a “mechanical fingerprint” of a materials response to contact deformation. Over the last few years, much attention has been focused on understanding the factors controlling the detailed shape of unloading curves so that parameters such as true contact area, Young's modulus, and an indentation hardness number can be derived. When the unloading curve is well behaved (by which we mean approximating to linear behavior, or alternatively, fitting a power-law relationship), then this approach can be very successful. However, when the test volume displays considerable elastic recovery as the load is removed [e.g., for many stiff hard materials and many inhomogeneous systems (e.g., those employing thin hard coatings)], then the unloading curve fits no existing model particularly well. This results in considerable difficulty in obtaining valid mechanical property data for these types of materials. An alternative approach, described here, is to attempt to understand the shapes of nanoindentation loading curve and thus quantitatively model the relationship between Young's modulus, indentation hardness, indenter geometry, and the resultant maximum displacement for a given load. This paper describes the development and refinement of a previous approach by Loubet et al1 originally suggested for a Vickers indenter, but applied here to understand the factors that control the shape of the loading curve during nanoindentation experiments with a pointed, trigonal (Berkovich) indenter. For a range of materials, the relationship P = Kmδ2 was found to describe the indenter displacement, δ, in terms of the applied load P. For each material, Km can be predicted from the Young's modulus (E) and the hardness (H). The result is that if either E or H is known, then the other may be calculated from the experimental loading curve. This approach provides an attractive alternative to finite element modeling and is a tractable approach for those cases where analysis of unloading curves is infeasible.

Influence of Ion Implantation on Tribo and Mechanical Behaviour of Duplex Hard Coatings

2010 ◽  
Author(s):  
Branko Skoric ◽  
Damir Kakas ◽  
Aleksandar Miletic
Keyword(s):  
Ion Implantation ◽  
Young’S Modulus ◽  
Physical Vapor Deposition ◽  
Young's Modulus ◽  
Elastic Recovery ◽  
Ion Beam ◽  
High Hardness ◽  
Hard Coatings ◽  
Tin Films ◽  
Unloading Stiffness

In this paper, we present the results of a study of TiN films which are deposited by a Physical Vapor Deposition and Ion Beam Assisted Deposition. In the present investigation the subsequent ion implantation was provided with N2+ ions. The ion implantation was applied to enhance the mechanical properties of surface. In the nanoindentation technique, hardness and Young’s modulus can be determined by the Oliver and Pharr method. Indentation was performed with CSM Nanohardness Tester. The results are analyzed in terms of load-displacement curves, hardness, Young’s modulus, unloading stiffness and elastic recovery The analysis of the indents was performed by Atomic Force Microscope. The stress determination follows the conventional sin2 Ψ method, using a X-ray diffractometer. A variety of analytic techniques were used for characterization, such as scratch test, calo test, SEM, AFM, XRD and EDAX. Therefore, by properly selecting the processing parameters, well-adherent TiN films with high hardness can be obtained on engineering steel substrates, and show a potential for engineering applications. The experimental results indicated that the mechanical hardness is elevated by penetration of nitrogen, whereas the Young’s modulus is significantly elevated.

scholarly journals Hardness, Young’s Modulus and Elastic Recovery in Magnetron Sputtered Amorphous AlMgB14 Films

Crystals ◽  
2020 ◽  
Vol 10 (9) ◽  
pp. 823
Author(s):  
Alexander M. Grishin
Keyword(s):  
Young’S Modulus ◽  
Indentation Size Effect ◽  
Young's Modulus ◽  
Elastic Recovery ◽  
Rf Power ◽  
Magnesium Boride ◽  
Wide Range ◽  
Aluminum Magnesium Boride ◽  
Optical And Mechanical Properties ◽  
Diamond Probe

We report optical and mechanical properties of hard aluminum magnesium boride films magnetron sputtered from a stoichiometric AlMgB14 ceramic target onto Corning® 1737 Glass and Si (100) wafers. High target sputtering rf-power and sufficiently short target-to-substrate distance appeared to be critical processing conditions. Amorphous AlMgB14 films demonstrate very strong indentation size effect (ISE): exceptionally high nanohardness H = 88 GPa and elastic Young’s modulus E* = 517 GPa at 26 nm of the diamond probe penetration depth and almost constant values, respectively, of about 35 GPa and 275 GPa starting at depths of about 2–3% of films’ thickness. For comparative analysis of elastic strain to failure index  H/E*, resistance to plastic deformation ratio H3/E*2 and elastic recovery ratio We were obtained in nanoindentation tests performed in a wide range of loading forces from 0.5 to 40 mN. High authentic numerical values of H = 50 GPa and E* = 340 GPa correlate with as low as only 10% of total energy dissipating through the plastic deformations.

A Phenomenological Model for the Hysteresis Behavior of Metal Sheets Subjected to Unloading/Reloading Cycles

2011 ◽  
Vol 133 (6) ◽  
Author(s):  
P.-A. Eggertsen ◽  
K. Mattiasson ◽  
J. Hertzman
Keyword(s):  
Young’S Modulus ◽  
Young's Modulus ◽  
Elastic Recovery ◽  
Yield Criterion ◽  
Experimental Investigations ◽  
Secant Modulus ◽  
New Model ◽  
Forming Simulation ◽  
Metal Sheets ◽  
Steel Grades

The springback phenomenon is defined as elastic recovery of the stresses produced during the forming of a material. An accurate prediction of the springback puts high demands on the material modeling during the forming simulation, as well as during the unloading simulation. In classic plasticity theory, the unloading of a material after plastic deformation is assumed to be linearly elastic with the stiffness equal to Young’s modulus. However, several experimental investigations have revealed that this is an incorrect assumption. The unloading and reloading stress–strain curves are in fact not even linear, but slightly curved, and the secant modulus of this nonlinear curve deviates from the initial Young’s modulus. More precisely, the secant modulus is degraded with increased plastic straining of the material. The main purpose of the present work has been to formulate a constitutive model that can accurately predict the unloading of a material. The new model is based on the classic elastic-plastic framework, and works together with any yield criterion and hardening evolution law. To determine the parameters of the new model, two different tests have been performed: unloading/reloading tests of uniaxially stretched specimens, and vibrometric tests of prestrained sheet strips. The performance of the model has been evaluated in simulations of the springback of simple U-bends and a drawbead example. Four different steel grades have been studied in the present investigation.

Transverse Young's Moduli and Cell Shapes in Coniferous Early Wood

Holzforschung ◽  
2002 ◽  
Vol 56 (1) ◽  
pp. 1-6 ◽  
Author(s):  
Ugai Watanabe ◽  
Minoru Fujita ◽  
Misato Norimoto
Keyword(s):  
Young’S Modulus ◽  
Young's Modulus ◽  
Bending Moment ◽  
Cell Models ◽  
Young’S Moduli ◽  
Cell Shapes ◽  
The Difference ◽  
Square Cells ◽  
Experimental Values ◽  
The Relationship

Summary The relationship between transverse Young's moduli and cell shapes in coniferous early wood was investigated using cell models constructed by two dimensional power spectrum analysis. The calculated values of tangential Young's modulus qualitatively explained the relationship between experimental values and density as well as the difference in experimental values among species. The calculated values of radial Young's modulus for the species having hexagonal cells agreed well with the experimental values, whereas, for the species having square cells, the calculated values were much larger than the experimental values. This result was ascribed to the fact that the bending moment on the radial cell wall of square cell models was calculated to be small. It is suggested that the asymmetrical shape of real wood cells or the behavior of nodes during ell deformation is an important factor in the mechanism of linear elastic deformation of wood cells.

Prediction of Springback in Metal Forming of Diaphragm of Automotive Horn Based on BPANN

2010 ◽  
Vol 139-141 ◽  
pp. 594-599
Author(s):  
Yan Qiu Zhang ◽  
Shu Yong Jiang ◽  
Yu Feng Zheng
Keyword(s):  
Young’S Modulus ◽  
Metal Forming ◽  
Young's Modulus ◽  
Steel Strip ◽  
Back Propagation ◽  
Spring Steel ◽  
Yield Ratio ◽  
Punch Radius ◽  
Cold Rolled ◽  
The Relationship

The spring steel strip 50CrVA which is cold rolled was applied to manufacture the diaphragm of the automotive horn by means of sheet metal forming. The combination of the experiments with back-propagation artificial neural network (BPANN) is used to solve the springback problem of the diaphragm. Experiments have shown that a 4-8-1 BPANN is able to predict the springback of the diaphragm successfully, and the network is able to model the relationship between the springback of the diaphragm and the process parameters rationally. BPANN simulation results and experimental ones have shown that the springback of the diaphragm is particularly influenced by such parameters as blank thickness, Young’s modulus, punch radius and yield ratio. Furthermore, the springback of the diaphragm decreases with the increase of blank thickness and Young’s modulus, but increases with the increase of punch radius and yield ratio.

Modified Model for Static Behavior of Microcantilever Gas Sensor Adsorbed with Monolayer Molecules

2011 ◽  
Vol 415-417 ◽  
pp. 455-459
Author(s):  
Xiao Ming Wang ◽  
Fei Wang ◽  
Xue Zeng Zhao ◽  
Da Lei Jing
Keyword(s):  
Young’S Modulus ◽  
Young's Modulus ◽  
Curvature Radius ◽  
Static Behavior ◽  
Neutral Layer ◽  
Modified Model ◽  
Adsorbed Molecules ◽  
Microcantilever Sensors ◽  
The Relationship ◽  
Layer Position

The modified static bending model of microcantilever with monolayer molecules has been established based on energy method, in which the change in neutral layer position caused by adsorption-induced stress has been considered. On this basis, we have analyzed the relationship between the bending curvature radius of a microcantilever with its thickness, Young’s modulus and molecule-molecule distance of adsorbed molecules when it is adsorbed with monolayer water molecules. Additionally, we have investigated the effect of change in neutral layer position on the static behavior of microcantilever sensors and have found that: 1) the bending curvature radius of microcantilever is affected by its Young’s modulus, thickness and distance of adsorbed molecules respectively; 2)the predicted error of bending curvature radius caused by the change in neutral layer position slightly increases with decreasing Young’s modulus and thickness, whereas the effect of distance between adsorbed molecules on the error is significant.

A New Method Developed for Brittle and Ductile Materials to Evaluate Mechanical Properties of a Lump Specimen in the Use of Indentation Test

2006 ◽  
Vol 129 (2) ◽  
pp. 284-292 ◽  
Author(s):  
Pal Jen Wei ◽  
Jen Fin Lin
Keyword(s):  
Yield Strength ◽  
Young’S Modulus ◽  
Young's Modulus ◽  
Elastic Recovery ◽  
Indentation Test ◽  
New Method ◽  
Ductile Materials ◽  
Conventional Material ◽  
Loading And Unloading ◽  
Logarithm Function

In this study, the load-depth (P‐h) relationships matching the experimental results of the nanoindentation tests exhibited at the subregions of small and large depths are obtained, respectively. The relationships associated with these two subregions are then linked by the hyperbolic logarithm function to attain a single expression that is applied in the evaluation of the specimen’s elastic recovery ability, as shown in the unloading process. A new method is developed in the present study to evaluate both Young’s modulus and the yield strength of either a ductile or brittle material through the uses of the appropriate P‐h relationships developed in the load and unloading processes. The results of the Young’s modulus and the yield strength achieved by the present method are compared to those obtained from the conventional material tests for a lump material. The scattering of the experimental data shown in the loading and unloading processes are also interpreted by different causes.

New expanding cavity model for indentation hardness including strain-hardening and indentation size effects

2006 ◽  
Vol 21 (5) ◽  
pp. 1317-1326 ◽  
Author(s):  
X.-L. Gao
Keyword(s):  
Strain Hardening ◽  
Young’S Modulus ◽  
Strain Gradient ◽  
Young's Modulus ◽  
Indentation Hardness ◽  
Cavity Model ◽  
Indentation Size ◽  
New Model ◽  
Plastic Materials ◽  
Classical Plasticity

An expanding cavity model (ECM) for determining indentation hardness of elastic–strain-hardening plastic materials is developed. The derivation is based on a strain gradient plasticity solution for an internally pressurized thick-walled spherical shell of an elastic linear-hardening material. Closed-form formulas are provided for both conical and spherical indentations. The formulas explicitly show that indentation hardness depends on Young's modulus, yield stress, strain-hardening index, and strain gradient coefficient of the indented material as well as on the geometry of the indenter. The newly formulated ECM can capture the indentation size effect, unlike classical plasticity based ECMs. The new model reduces to existing classical plasticity based ECMs (including Johnson's ECM for elastic-perfectly plastic materials) when the strain gradient effect is not considered. The presently developed ECM is validated by comparing with existing experimental hardness data. The numerical results obtained using the new model reveal that the hardness is indeed indentation size dependent when the indentation radius is very small: the smaller the indentation, the larger the hardness. Also, the indentation hardness is seen to increase with the Young's modulus and strain-hardening level of the indented material for both conical and spherical indentations. The strain-hardening effect on the hardness is observed to be significant for materials having strong strain-hardening characteristics. In addition, it is found that the indentation hardness increases with decreasing cone angle of the conical indenter or decreasing radius of the spherical indenter. These trends agree with existing experimental observations and model predictions.

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