Influence of Substrate Hardness on the Response of W–C–Co-coated Samples to Depth-sensing Indentation

2000 ◽  
Vol 15 (8) ◽  
pp. 1766-1772 ◽  
Author(s):  
J. V. Fernandes ◽  
A. C. Trindade ◽  
L. F. Menezes ◽  
A. Cavaleiro
Keyword(s):  
Indentation Depth ◽  
Critical Value ◽  
The Other ◽  
Differential Analysis ◽  
Depth Sensing ◽  
Indentation Tests ◽  
Influence Of Substrate ◽  
Film Substrate ◽  
Substrate Hardness ◽  
Measured Hardness

Depth-sensing indentation tests were used to determine the hardness of amorphous W–C–Co coatings deposited on different steel and copper substrates. The hardness of the film, Hf, was chosen to be always greater than the hardness of the substrate Hs and within the range Hf/Hs = 2 to 18.5. The influence of the ratio Hf/Hs on the ratio (t/hD)C between the film thickness t and the critical value of the indentation depth (hD)C, for which the substrate starts to deform plastically, was studied. Two independent methods were used to determine (hD)C values. One utilized the differential analysis of the loading part of the indentation curve, and the other was based on the plot of (Hc – Hs)/(Hf − Hs) versus t/(hD), Hc being the measured hardness of the film/substrate composite at a given indentation depth (hD). A good correlation between both methods was found.

Shape Effects of Indenter on the Depth-Sensing Indentation

2010 ◽  
Vol 177 ◽  
pp. 105-108
Author(s):  
Xin Yong Shi ◽  
Li Zhong Liu ◽  
Yi Wang Bao
Keyword(s):  
Displacement Curve ◽  
Theoretic Analysis ◽  
Modulus Ratio ◽  
Depth Sensing ◽  
Flat Punch ◽  
Element Simulation ◽  
Reduced Modulus ◽  
Shape Effects ◽  
Indentation Tests ◽  
Measured Hardness

It is revealed that the conventional reduced modulus used in depth-sensing indentation tests is invalid for a flat-ended cylindrical indenter due to the fact that the contact area during the loading is a constant irrelative to load. The load-displacement curve of flat punch is related to the length of the punch and the ratio of the elastic modulus of the indenter to the specimen (the modulus ratio Ei/E). Furthermore, theoretic analysis and finite element simulation demonstrated that, for conical indenter, the measured hardness from depth-sensing indentation tests would increase with increasing modulus ratio because the load increased with the ratio for the same displacement.

The Role of Indentation Depth on the Measured Hardness of Materials

1993 ◽  
Vol 308 ◽  
Author(s):  
Melissa Shell De Guzman ◽  
Gabi Neubauer ◽  
Paul Flinn ◽  
William D. Nix
Keyword(s):  
Strain Hardening ◽  
Amorphous Materials ◽  
Indentation Depth ◽  
Density Of Dislocations ◽  
Real Material ◽  
Dislocation Densities ◽  
Indentation Tests ◽  
Micro Indentation ◽  
Measured Hardness

ABSTRACTUltra micro-indentation tests on Ni and Cu samples showed increasing hardness with decreasing penetration depth over a range from 200 to 2000 nm. The results suggest increased strain hardening with decreased indentation depth. To establish that this is a real material effect, a series of tests were conducted on amorphous materials, for which strain hardening is not expected. The hardness of Metglas® was found to be independent of depth. A simple model of the dislocation densities produced under the indenter tip describes the data well. The model is based on the fact that the high density of dislocations expected under a shallow indentation would cause an increase in measured hardness. At large depths, the density of geometrically necessary dislocations is sufficiently small to have little effect on hardness, and the measured hardness approaches the intrinsic hardness of the material.

Indentation responses of time-dependent films on stiff substrates

2004 ◽  
Vol 19 (8) ◽  
pp. 2487-2497 ◽  
Author(s):  
Michelle L. Oyen ◽  
Robert F. Cook ◽  
John A. Emerson ◽  
Neville R. Moody
Keyword(s):  
Peak Load ◽  
Elastic Response ◽  
Depth Sensing ◽  
Indentation Tests ◽  
Unloading Rate ◽  
Loading And Unloading ◽  
Load Displacement ◽  
Film Substrate ◽  
Single Set ◽  
Substrate Influence

A viscous-elastic-plastic indentation model was extended to a thin-film system, including the effect of stiffening due to a substrate of greater modulus. The system model includes a total of five material parameters: three for the film response (modulus, hardness, and time constant), one for the substrate response (modulus), and one representing the length-scale associated with the film-substrate interface. The substrate influence is incorporated into the elastic response of the film through a depth-weighted elastic modulus (based on a series sum of film and substrate contributions). Constant loading- and unloading-rate depth-sensing indentation tests were performed on polymer films on glass or metal substrates. Evidence of substrate influence was examined by normalization of the load-displacement traces. Comparisons were made between the model and experiments for indentation tests at different peak load levels and with varying degrees of substrate influence. A single set of five parameters was sufficient to characterize and predict the experimental load-displacement data over a large range of peak load levels and corresponding degrees of substrate influence.

scholarly journals A Quantitative Model for Interpreting Nanometer Scale Hardness Measurements of Thin Films

1993 ◽  
Vol 308 ◽  
Author(s):  
W.H. Poisl ◽  
B.D. Fabes ◽  
W.C. Oliver
Keyword(s):  
Thin Films ◽  
Interfacial Strength ◽  
Quantitative Model ◽  
Carbon Layer ◽  
Nanometer Scale ◽  
Depth Sensing ◽  
Sapphire Substrates ◽  
Measured Change ◽  
Film Substrate ◽  
Measured Hardness

ABSTRACTA model has been developed to determine the hardness of thin films from the measured change in hardness with indenter displacement using a depth-sensing indentation instrument. The model is developed by dividing the measured hardness into film and substrate contributions based on the projected areas of both the film and substrate under the indenter. The model incorporates constraints on the deformation of the film by the surrounding material in the film, the substrate, and friction at the indenter/film and film/substrate interfaces. These constraints increase the pressure that the film can withstand and account for the increase in measured hardness as the indenter approaches the substrate.The model is evaluated by fitting the predicted hardness versus depth curves to data obtained from titanium and Ta2O5 films of varying thicknesses on sapphire substrates. The model predicts a lower interfacial strength for Ta2O5 films on sapphire with a carbon layer between the film and the substrate than that obtained for a film without an interfacial carbon layer.

Effect of Applied and Residual Stresses on the Analysis of Mechanical Properties by Means of Instrumented Indentation Techniques

2005 ◽  
Vol 490-491 ◽  
pp. 454-459 ◽  
Author(s):  
Jens Gibmeier ◽  
Stefan Hartmann ◽  
Berthold Scholtes
Keyword(s):  
Mechanical Properties ◽  
Residual Stresses ◽  
Indentation Depth ◽  
Experimental Investigations ◽  
Indentation Testing ◽  
Instrumented Indentation ◽  
Depth Sensing ◽  
Initial State ◽  
Indentation Tests ◽  
Prestressed Materials

Various methods have been proposed in recent years for the determination of mechanical properties of a material by using instrumented indentation testing. These load and depth sensing indentation techniques imply the measurement of a characteristic load-indentation depth curve by the aid of which numerous materials properties can be extracted. On the other hand in many publications the effect of applied or residual stresses on the results of hardness readings is investigated. Methods are proposed to estimate applied or residual stresses by means of instrumented indentation testing. Based on this obvious inconsistency between these procedures on the use of information of instrumented hardness testing the influence of residual stresses as well as applied stresses on continuous microhardness readings is systematically investigated for steel samples. Experimental investigations were supplemented by finite element simulations of ball indentation tests on equi-biaxially prestressed materials states. These simulations show that the registered force-indentation depth curves as well as the geometry of the indentations are affected by loading and residual stresses in a characteristic way. For hardness values changes of up to 35% are determined with reference to the unstressed initial state.

MEASUREMENT OF THE HARDNESS OF ULTRA-THIN FILMS BY THE FIRST DERIVATIVE OF LOAD-DISPLACEMENT CURVE FROM NANOINDENTATION DATA

2010 ◽  
Vol 24 (01n02) ◽  
pp. 256-266 ◽  
Author(s):  
AMIT KUMAR ◽  
KAIYANG ZENG
Keyword(s):  
Thin Films ◽  
Indentation Depth ◽  
Displacement Curve ◽  
Bulk Materials ◽  
Alternative Analysis ◽  
Soft Substrate ◽  
Substrate Effects ◽  
Film Substrate ◽  
Hardness Values ◽  
Measured Hardness

The commonly-used nanoindentation experiments for measuring hardness of thin films may not give the accurate results when the thickness of the film is in the range of few hundred nanometers or less due to the unavoidable substrate effects. The available analysis methods usually work well when the indentation depth is less than one tenth of the total thickness of the film; otherwise, it is very difficult to determine the film-only properties without substrate effects. This work proposes an alternative analysis to measure the hardness of ultra-thin film from nanoindentation data. This method is tested for numbers of bulk materials and the results agreed well with literature reported values; the method is then applied to thin films. It is found that this analysis can give very accurate results for different kind of film-substrate systems such as soft-films on hard-substrate and hard-film on soft-substrate. As the proposed method is based on the measurement of hardness at each indentation step therefore, it is also capable to show at what indentation depth the substrate starts affecting the indentation-measured hardness values.

Strain and Stress Distribution in Vickers Indentation of Coated Materials

2006 ◽  
Vol 514-516 ◽  
pp. 1472-1476
Author(s):  
Jorge M. Antunes ◽  
Nataliya A. Sakharova ◽  
José Valdemar Fernandes ◽  
Luís Filipe Menezes
Keyword(s):  
Thin Films ◽  
Mechanical Properties ◽  
Numerical Simulation ◽  
Young’S Modulus ◽  
Indentation Depth ◽  
Young's Modulus ◽  
Three Dimensional ◽  
Depth Sensing ◽  
Coated Materials ◽  
Film Substrate

Depth sensing indentation equipment allows the mechanical properties of thin films to be easily determined, particularly the hardness and Young’s modulus. In order to minimize the influence of the substrate on the measured properties, the indentation depth must be limited to a small fraction of the film’s thickness. However, for very thin films, the determination of the contribution of the substrate and the film to the measured mechanical properties becomes a hard task, because both deform plastically. The numerical simulation of ultramicrohardness tests can be a helpful tool towards better understanding of the influence of the parameters involved in the mechanical characterization of thin films. For this purpose, a three-dimensional numerical simulation home code, HAFILM, was used to simulate ultramicrohardness tests on coated substrates. Materials with different Young’s modulus film/substrate ratios were tested. Analyses of strain and stress distributions for several indentation depth values were performed, in order to clarify the composite behaviour.

Action-Minimizing Curves for Tonelli Lagrangians

2017 ◽  
Author(s):  
Alfonso Sorrentino
Keyword(s):  
Critical Value ◽  
The Other ◽  
Invariant Sets ◽  
Simple Pendulum ◽  
New Concepts ◽  
Peierls Barrier ◽  
Average Action

This chapter discusses the notion of action-minimizing orbits. In particular, it defines the other two families of invariant sets, the so-called Aubry and Mañé sets. It explains their main dynamical and symplectic properties, comparing them with the results obtained in the preceding chapter for the Mather sets. The relation between these new invariant sets and the Mather sets is described. As a by-product, the chapter introduces the Mañé's potential, Peierls' barrier, and Mañé's critical value. It discusses their properties thoroughly. In particular, it highlights how this critical value is related to the minimal average action and describes these new concepts in the case of the simple pendulum.

scholarly journals Analysis of depth-sensing indentation tests with a Knoop indenter

2001 ◽  
Vol 16 (6) ◽  
pp. 1660-1667 ◽  
Author(s):  
L. Riester ◽  
T. J. Bell ◽  
A. C. Fischer-Cripps
Keyword(s):  
Elastic Modulus ◽  
Elastic Recovery ◽  
Indentation Test ◽  
New Method ◽  
Short Axis ◽  
Depth Sensing ◽  
Specimen Material ◽  
Indentation Tests ◽  
Conventional Methods ◽  
Knoop Indenter

The present work shows how data obtained in a depth-sensing indentation test using a Knoop indenter may be analyzed to provide elastic modulus and hardness of the specimen material. The method takes into account the elastic recovery along the direction of the short axis of the residual impression as the indenter is removed. If elastic recovery is not accounted for, the elastic modulus and hardness are overestimated by an amount that depends on the ratio of E/H of the specimen material. The new method of analysis expresses the elastic recovery of the short diagonal of the residual impression into an equivalent face angle for one side of the Knoop indenter. Conventional methods of analysis using this corrected angle provide results for modulus and hardness that are consistent with those obtained with other types of indenters.

Comparison of Means: An F Test Followed by a Modified Multiple Range Procedure

1979 ◽  
Vol 4 (1) ◽  
pp. 14-23 ◽  
Author(s):  
Juliet Popper Shaffer
Keyword(s):  
Error Control ◽  
Type I Error ◽  
Critical Value ◽  
The Other ◽  
Type I ◽  
F Test ◽  
Range Test

If used only when a preliminary F test yields significance, the usual multiple range procedures can be modified to increase the probability of detecting differences without changing the control of Type I error. The modification consists of a reduction in the critical value when comparing the largest and smallest means. Equivalence of modified and unmodified procedures in error control is demonstrated. The modified procedure is also compared with the alternative of using the unmodified range test without a preliminary F test, and it is shown that each has advantages over the other under some circumstances.

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