Determination of elastic modulus and hardness of viscoelastic-plastic materials by instrumented indentation under harmonic load

2005 ◽  
Vol 20 (10) ◽  
pp. 2660-2669 ◽  
Author(s):  
J. Menčík ◽  
G. Rauchs ◽  
J. Bardon ◽  
A. Riche
Keyword(s):  
Elastic Modulus ◽  
Contact Stiffness ◽  
Harmonic Signal ◽  
Specific Response ◽  
Harmonic Load ◽  
Depth Sensing ◽  
Plastic Materials ◽  
Continuous Stiffness Measurement ◽  
Unloading Stiffness ◽  
Monotonic Load

When determining elastic modulus and hardness of viscoelastic-plastic materials by depth-sensing indentation, one must respect their specific response. In the monotonic load-unload testing mode, the unloading should be preceded by a dwell mitigating the influence of the delayed deforming. The continuous stiffness measurement (CSM) mode, with a small harmonic signal added to the basic monotonic load, enables continuous measurement of harmonic contact stiffness and mechanical properties as a function of depth. However, the contact depth and area in this mode actually depend on the slow (monotonic) component of the loading and should be determined not from the harmonic contact stiffness but from the unloading stiffness; otherwise, the calculated elastic modulus and mean contact pressure will be incorrect. This paper provides the formulae for these calculations, defines special characteristics—such as apparent dynamic hardness and the index of sensitivity to harmonic loading—and shows how to improve results by smoothing the harmonic stiffness curve. The proposed methods are illustrated through nanoindentation tests of polymethyl methacrylate.

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.

Influences of pileup on the measurement of mechanical properties by load and depth sensing indentation techniques

1998 ◽  
Vol 13 (4) ◽  
pp. 1049-1058 ◽  
Author(s):  
A. Bolshakov ◽  
G. M. Pharr
Keyword(s):  
Finite Element ◽  
Elastic Modulus ◽  
Indentation Load ◽  
Depth Sensing ◽  
Element Mesh ◽  
Plastic Materials ◽  
Element Simulation ◽  
Load Displacement ◽  
Elastic Plastic Materials ◽  
True Contact

Finite element simulation of conical indentation of a wide variety of elastic-plastic materials has been used to investigate the influences of pileup on the accuracy with which hardness and elastic modulus can be measured by load and depth-sensing indentation techniques. The key parameter in the investigation is the contact area, which can be determined from the finite element results either by applying standard analysis procedures to the simulated indentation load-displacement data, as would be done in an experiment, or more directly, by examination of the contact profiles in the finite element mesh. Depending on the pileup behavior of the material, these two areas may be very different. When pileup is large, the areas deduced from analyses of the load-displacement curves underestimate the true contact areas by as much as 60%. This, in turn, leads to overestimations of the hardness and elastic modulus. The conditions under which the errors are significant are identified, and it is shown how parameters measured from the indentation load-displacement data can be used to identify when pileup is an important factor.

Use of combined elastic modulus in the analysis of depth-sensing indentation data

2001 ◽  
Vol 16 (11) ◽  
pp. 3050-3052 ◽  
Author(s):  
A. C. Fischer-Cripps
Keyword(s):  
Elastic Modulus ◽  
Test Data ◽  
Nanoindentation Test ◽  
Depth Sensing ◽  
True Value ◽  
Methods Of Analysis ◽  
Reduced Modulus ◽  
Unloading Stiffness ◽  
Depth Response

It is shown that the substitution of reduced modulus for specimen modulus in the analysis equations for nanoindentation test data is valid. The methods of analysis use the slope of the unloading force–depth response which is assumed to be elastic. Because of this utilization of the slope or unloading stiffness, it makes no difference whether or not the deflection of the indenter is accommodated explicitly or transferred to that occurring within the specimen by artificially reducing the specimen modulus from its true value to lower value, the reduced modulus.

Characterization of Surface Layer of Silicon Wafer by Using Nano Indenter

2007 ◽  
Author(s):  
Yu-Li Sun ◽  
Dun-Wen Zuo ◽  
Yong-Wei Zhu ◽  
Feng Xu ◽  
Min Wang
Keyword(s):  
Elastic Modulus ◽  
Silicon Wafer ◽  
Bulk Material ◽  
Contact Stiffness ◽  
Indentation Test ◽  
Oxide Coating ◽  
Stiffness Measurement ◽  
Contact Depth ◽  
Continuous Stiffness Measurement

Mechanical properties of the silicon wafer are evaluated by a nano indenter system with the continuous stiffness measurement (CSM) technique. Contact stiffness, hardness and elastic modulus of the silicon wafer are continuously measured during the loading in an indentation test. The results show that when the contact depth is between 20 and 32 nm, its contact stiffness is linear with the contact depth, and its hardness and elastic modulus keep constant at 10.2 GPa and 140.3 GPa respectively, which belong to the oxide coating of the silicon wafer. When the contact depth is between 32 and 60 nm, its contact stiffness is not linear with the contact depth, and the hardness and elastic modulus increase rapidly with the contact depth, because they are affected by the bulk material. When the contact depth is over 60 nm, the contact stiffness of the silicon wafer is linear with the contact depth again, and the hardness and elastic modulus keep constant at 12.5 GPa and 165.6 GPa respectively, which belong to the silicon wafer, the bulk material.

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.

On Determining Elastic Modulus from Instrumented Indentation

2013 ◽  
Vol 668 ◽  
pp. 616-620
Author(s):  
Shuai Huang ◽  
Huang Yuan
Keyword(s):  
Finite Element ◽  
Elastic Modulus ◽  
Plastic Material ◽  
Instrumented Indentation ◽  
Computational Simulations ◽  
Elastic Plastic ◽  
Modified Method ◽  
Plastic Materials ◽  
Elastic Plastic Material ◽  
Elastic Plastic Materials

Computational simulations of indentations in elastic-plastic materials showed overestimate in determining elastic modulus using the Oliver & Pharr’s method. Deviations significantly increase with decreasing material hardening. Based on extensive finite element computations the correlation between elastic-plastic material property and indentation has been carried out. A modified method was introduced for estimating elastic modulus from dimensional analysis associated with indentation data. Experimental verifications confirm that the new method produces more accurate prediction of elastic modulus than the Oliver & Pharr’s method.

Contact stiffness depth-sensing indentation: Understanding of material properties of thin films attached to substrates

2017 ◽  
Vol 114 ◽  
pp. 172-179 ◽  
Author(s):  
Ivan I. Argatov ◽  
Feodor M. Borodich ◽  
Svetlana A. Epshtein ◽  
Elena L. Kossovich
Keyword(s):  
Thin Films ◽  
Material Properties ◽  
Contact Stiffness ◽  
Depth Sensing

Interaction Model for “Shelled Particles” and Small-Strain Modulus of Granular Materials

2018 ◽  
Vol 85 (10) ◽  
Author(s):  
Shun-hua Zhou ◽  
Peijun Guo ◽  
Dieter F. E. Stolle
Keyword(s):  
Elastic Modulus ◽  
Contact Stiffness ◽  
Scaling Law ◽  
Interaction Model ◽  
Contact Problems ◽  
Hertzian Contact ◽  
Spherical Particles ◽  
Thin Coating ◽  
Normal Contact ◽  
Laboratory Test Results

The elastic modulus of a granular assembly composed of spherical particles in Hertzian contact usually has a scaling law with the mean effective pressure p as K∼G∼p1/3. Laboratory test results, however, reveal that the value of the exponent is generally around 1/2 for most sands and gravels, but it is much higher for reclaimed asphalt concrete composed of particles coated by a thin layer of asphalt binder and even approaching unity for aggregates consisting of crushed stone. By assuming that a particle is coated with a thin soft deteriorated layer, an energy-based simple approach is proposed for thin-coating contact problems. Based on the features of the surface layer, the normal contact stiffness between two spheres varies with the contact force following kn∼Fnm and m∈[1/3,  1], with m=1/3 for Hertzian contact, m=1/2 soft thin-coating contact, m=2/3 for incompressible soft thin-coating, and m=1 for spheres with rough surfaces. Correspondingly, the elastic modulus of a random granular packing is proportional to pm with m∈[1/3,  1].

Numerical study on the dynamic characteristics of water-lubricated rubber bearing under asperity contact

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Guo Xiang ◽  
Yijia Wang ◽  
Cheng Wang ◽  
Zhongliang Lv
Keyword(s):  
Elastic Modulus ◽  
Contact Stiffness ◽  
Water Film ◽  
Radial Clearance ◽  
Asperity Contact ◽  
Stiffness Coefficient ◽  
Content Type ◽  
Damping Coefficients ◽  
Rubber Bearing ◽  
Stiffness And Damping

Purpose In this study, the dynamic characteristics of the water-lubricated rubber bearing considering asperity contact are numerically studied, including water-film stiffness and damping coefficients and plastic-elastic contact stiffness coefficient. Design/methodology/approach The Kogut-Etsion elastic-plastic contact model is applied to calculate the contact stiffness coefficient at the bearing-bush interface and the perturbed method is used to calculate the stiffness and damping coefficients of water-film. In addition, the rubber deformation is determined by the finite element method (FEM) during the simulation. Parametric studies are conducted to assess the effects of the radial clearance, rubber thickness and elastic modulus on the dynamic characteristic of water-lubricated rubber bearing. Findings Numerical results indicate that stiffness and damping coefficients of water film and the contact stiffness of asperity are increased with the decreasing of the radial clearance and the dynamic coefficients are less sensitive to the rubber thickness compared with the elastic modulus of rubber. Furthermore, due to the existed groove, a sudden change of the water film direct stiffness and damping coefficients is observed when the eccentricity ratio ranges from 0.6 to 1.0. Originality/value It is expected this study can provide more information to establish a dynamic equation of water-lubricated rubber bearings exposed to mixed lubrication conditions.

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