Comment to paper “Penetration depth and tip radius dependence on the correction factor in nanoindentation measurements” by J.M. Meza et al. [J. Mater. Res. 23(3), 725 (2008)]

2012 ◽  
Vol 27 (8) ◽  
pp. 1205-1207 ◽  
Author(s):  
Karsten Durst ◽  
Hamad ur Rehman ◽  
Benoit Merle
Keyword(s):  
Finite Element ◽  
Penetration Depth ◽  
Correction Factor ◽  
Elastic Material ◽  
Contact Area ◽  
Contact Stiffness ◽  
Fe Analysis ◽  
Tip Radius ◽  
True Contact Area ◽  
True Contact

[Meza et al. J. Mater. Res.23(3), 725 (2008)] recently claimed that the correction factor beta for the Sneddon equation, used for the evaluation of nanoindentation load-displacement data, is strongly depth- and tip-shape-dependent. Meza et al. used finite element (FE) analysis to simulate the contact between conical or spheroconical indenters, and an elastic material. They calculated the beta factor by comparing the simulated contact stiffness with Sneddon’s prediction for conical indenters. Their analysis is misleading, and it is shown here that by applying the general Sneddon equation, taking into account the true contact area, an almost constant and depth-independent beta factor is obtained for conical, spherical and spheroconical indenter geometries.

A response to—“Comment on the evaluation of the constant β relating the contact stiffness to the contact area in nanoindentation for sphero-conical indenters:” Comment to paper “Penetration depth and tip radius dependence on the correction factor in nanoindentation measurements” by J.M. Meza et al. [J. Mater. Res. 23(3), 725 (2008)]

2012 ◽  
Vol 27 (8) ◽  
pp. 1208-1210
Author(s):  
Juan Manuel Meza ◽  
Fazilay Abbes ◽  
Jaime Alexis Garcia Guzman ◽  
Michel Troyon
Keyword(s):  
Penetration Depth ◽  
Correction Factor ◽  
Contact Area ◽  
Contact Stiffness ◽  
Depth Range ◽  
Dimensionless Analysis ◽  
Plastic Materials ◽  
Variation Range ◽  
Elastic Plastic Materials ◽  
Tip Radius

The signification of the correction factor β that we defined for elastic material [J.M. Meza et al. J. Mater. Res.23(3), 725, (2008)] does not correspond to that of factor β in the Sneddon relationship between unloading contact stiffness, elastic modulus, and contact area as remarked by Durst et al. in their Comment (doi:10.1557/jmr.2012.41). To complete the results of Durst et al., the calculation of β is extended to a larger penetration depth range. It is shown that β depends on the depth to tip radius ratio, h/R, and on the Poisson’s ratio according to dimensionless analysis. The variation range of β is about 1.02–1.09 for 0.3 < h/R < 3 for purely elastic materials but can be much larger in case of elastic–plastic materials as shown [F. Abbes et al. J. Micromech. Microeng.20, 65003 (2010)].

Penetration depth and tip radius dependence on the correction factor in nanoindentation measurements

2008 ◽  
Vol 23 (3) ◽  
pp. 725-731 ◽  
Author(s):  
J.M. Meza ◽  
F. Abbes ◽  
M. Troyon
Keyword(s):  
Penetration Depth ◽  
Correction Factor ◽  
Contact Stiffness ◽  
Nanoindentation Test ◽  
Simple Analytical Model ◽  
Element Analysis ◽  
Maximum Penetration Depth ◽  
Maximum Penetration ◽  
Tip Radius ◽  
Indenter Geometry

Dimensional analysis is used to show that the maximum penetration depth and the tip radius affect the β correction factor appearing in the Sneddon relationship between unloading contact stiffness, contact area, and elastic modulus. A simple analytical model based on elasticity theory is derived that predicts the variation of β with penetration depth. This model shows that β increases at low penetration depth and decreases with the tip radius. The β(h) curve given by the model is compared with that calculated by finite element analysis for an elastic material and also with that deduced from experimental measurements performed on fused quartz with two Berkovich indenters: a sharp one and a blunted one. It is also demonstrated that the correction factor can be expressed as two multiplicative contributions, a contribution related to the mechanical properties of the material and a contribution related to the indenter geometry. Implications of these findings on nanoindentation test are 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 Evolution of the True Contact Area of Laser Textured Tungsten Under Dry Sliding Conditions

2019 ◽  
Vol 5 ◽  
Author(s):  
Björn Lechthaler ◽  
Georg Ochs ◽  
Frank Mücklich ◽  
Martin Dienwiebel
Keyword(s):  
Contact Area ◽  
Dry Sliding ◽  
True Contact Area ◽  
True Contact

scholarly journals Sliding-induced adhesion of stiff polymer microfibre arrays. I. Macroscale behaviour

2008 ◽  
Vol 5 (25) ◽  
pp. 835-844 ◽  
Author(s):  
Jongho Lee ◽  
Carmel Majidi ◽  
Bryan Schubert ◽  
Ronald S Fearing
Keyword(s):  
Elastic Modulus ◽  
Contact Area ◽  
Shear Force ◽  
Contact Region ◽  
Pure Shear ◽  
Shear Loading ◽  
High Shear ◽  
Polypropylene Fibres ◽  
True Contact Area ◽  
True Contact

Gecko-inspired microfibre arrays with 42 million polypropylene fibres cm −2 (each fibre with elastic modulus 1 GPa, length 20 μm and diameter 0.6 μm) were fabricated and tested under pure shear loading conditions, after removing a preload of less than 0.1 N cm −2 . After sliding to engage fibres, 2 cm 2 patches developed up to 4 N of shear force with an estimated contact region of 0.44 cm 2 . The control unfibrillated surface had no measurable shear force. For comparison, a natural setal patch tested under the same conditions on smooth glass showed approximately seven times greater shear per unit estimated contact region. Similar to gecko fibre arrays, the synthetic patch maintains contact and increases shear force with sliding. The high shear force observed (approx. 210 nN per fibre) suggests that fibres are in side contact, providing a larger true contact area than would be obtained by tip contact. Shear force increased over the course of repeated tests for synthetic patches, suggesting deformation of fibres into more favourable conformations.

The Role of Diffusion of Polymer Chains in the Mechanism of Adhesion and Autohesion of Rubbers

1957 ◽  
Vol 30 (3) ◽  
pp. 837-846 ◽  
Author(s):  
B. V. Deryagin ◽  
S. K. Zherebkov ◽  
A. M. Medvedeva
Keyword(s):  
Mechanical Properties ◽  
Double Layer ◽  
Contact Area ◽  
Electric Double Layer ◽  
Contact Time ◽  
Diffusion Processes ◽  
The Other ◽  
Shearing Strength ◽  
True Contact Area ◽  
True Contact

Abstract 1. The researches so far published on the autohesion of polymers do not make it possible to isolate the influence of the mechanical properties of rubbers, which determine the true area of contact, from the influence of polymer chain diffusion. 2. Studies of the autohesion of thin films of rubber applied by the drain-off method to quartz threads, in relation to the film thickness and contact time, show that for films less than 3.10−5 cm. thick the adhesion force is small and varies very little with contact time. This proves, on the one hand, that in this instance the contact area is small (which is obvious) and does not increase with time, and on the other hand, that diffusion processes play no part in the autohesion of films of this thickness. 3. The effects which depend on mechanical properties and on the specific interaction (per unit area of true contact) between specimens may be separated if the measured values of adhesion between all possible combinations of pairs of rubbers are compared both with their compatibilities, and with their autohesion. 4. The measurements of the adhesional shearing strength of combinations of different pairs of polymers, carried out for this purpose, showed that the results for Butyl rubber may be interpreted on the assumption that diffusion processes do not play any appreciable role and that the adhesion strength is determined both by the true contact area, which depends on the mechanical properties of the corresponding polymer specimens, and also by the influence of forces associated with the electric double layer. 5. For the other rubbers the results may be interpreted only on the assumption that diffusion processes play a significant part. For similar polarities, T12/T11&gt;1 and for dissimilar polarities, T12/T11&lt;1. 6. General conclusion : autohesion and mutual adhesion of rubbers is determined both by mechanical properties, which determine the true contact area, and by diffusional properties. The latter are by no means always decisive. The electric double layer also probably influences the adhesional shearing strength in some instances. It is even more likely to play a role in some cases in measurements of the work of separation of two layers.

A fractal model of contact between rough surfaces for a complete loading–unloading process

2020 ◽  
Vol 234 (14) ◽  
pp. 2923-2935
Author(s):  
Yuan Yuan ◽  
Kuo Xu ◽  
Ke Zhao
Keyword(s):  
Size Distribution ◽  
Contact Area ◽  
Rough Surfaces ◽  
Contact Process ◽  
Distribution Functions ◽  
Contact Load ◽  
Elastic Behavior ◽  
Loading Process ◽  
True Contact Area ◽  
True Contact

The mechanical properties of contact between rough surfaces play an important role in the reliability of the electromechanical system. In order to improve the design accuracy of precision instruments, an elastic-plastic contact model for three-dimensional rough surfaces based on the fractal theory is developed for a complete loading–unloading process based on the Majumdar and Bhushan model. The truncation size distribution functions of asperities for different values of asperity level in the loading process are given. Relationships between true contact area and total contact load in the complete loading–unloading process are obtained according to the truncation size distribution functions of asperities. The results show the range of asperity levels has significant effects on contact mechanical behaviors of fractal rough surfaces. When the first six levels of asperities do not exceed the critical elastic level, the fractal rough surfaces exhibit elastic behavior in a complete contact process, and the load–area relationships in the loading and unloading processes are coincident approximately. When the critical elastic level is less than the minimum level of asperity, the inelastic deformation begins to appear in fractal rough surfaces and the true contact area during the unloading process is always greater than the true area during the loading process for a given total contact load. In comparison with the K-K-E model, the present model is proved to be reasonable.

Metallic wear

1952 ◽  
Vol 212 (1111) ◽  
pp. 470-477 ◽  
Keyword(s):  
Contact Area ◽  
Large Fraction ◽  
Wear Particle ◽  
Wear Particles ◽  
Wear Model ◽  
Real Area Of Contact ◽  
Cylindrical Metal ◽  
Proportional Increase ◽  
True Contact Area ◽  
True Contact

This paper describes experiments on the wear between a cylindrical metal pin and a hardened steel disk. Under steady-state conditions at light loads it is found that the volume V of material worn away is proportional to the load W, and the length L of path traversed so that V = k'LW . Since the real area of contact A may be written as A = W/P m , where P m is a strength property of the pin, the wear equation may be rewritten V = k'LA /P m = kLA , where k is a constant for the surfaces. This relation suggests that, of the welded junctions formed at the interface and sheared during sliding a constant fraction is detached to form the wear particles. On this View an increase in load produces a proportional increase in the number of welds each of which remains approximately of constant size. This is supported by an examination of the wear particles. This mechanism would seem preferable to the atomic wear model suggested by Holm, which also yields a wear equation of the form V = kLA . At higher loads, in excess of an average pressure about one-third the hardness of the pin, a large increase in the wear rate is observed. It is suggested that this is primarily due to the fact that the true contact area has become such a large fraction of the apparent contact area which is available that a loose wear particle once formed is not able to get away without producing further particles in a self-accelerating process. These results are discussed in relation to the practical problem of running-in newly assembled machine parts.

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