Contact Analysis Considering Surface Stress and Surface Elasticity: Increase of Indentation Hardness and Yield Stress

2012 ◽  
Author(s):  
Takao Hayashi ◽  
Hideo Koguchi
Keyword(s):  
Yield Stress ◽  
Surface Stress ◽  
Indentation Depth ◽  
Surface Elasticity ◽  
Elastic Half Space ◽  
Contact Analysis ◽  
Indentation Hardness ◽  
Indentation Modulus ◽  
Transform Method ◽  
Anisotropic Elastic

An increase in indentation hardness with decreasing indentation depth has been observed in nanoindentation studies. It is known as the indentation size effect. The indentation modulus in Molecular Dynamics (MD) contact analysis is larger than that in theoretical analysis (Hertz contact theory). In this paper, elasto-plastic contact analysis for an anisotropic elastic half-space is performed using the surface Green’s function considering surface stress and surface elasticity. A contact analysis is conducted to investigate the effect of surface stress on yield stress and indentation hardness. The discrete convolution, fast Fourier transform method and conjugate gradient method are applied to the contact analysis. The hardening model of the elasto-perfect plastic law is used in this study. The yield stress is determined so that a contact area considering surface stress is agreed with the one ignoring surface stress. Then, the yield stress ignoring surface stress and surface elasticity fixed at a constant. It is found that the yield stress considering surface stress and surface elasticity increases with decreasing the indentation depth. The indentation hardness considering surface stress and surface elasticity is calculated using the determined yield stress. The effects of surface stress and surface elasticity on the indentation hardness and the yield stress is discussed.

Nanoindentation hardness of a Steigmann–Ogden surface bounding an elastic half-space

2018 ◽  
Vol 24 (9) ◽  
pp. 2754-2766 ◽  
Author(s):  
Xiaobao Li ◽  
Changwen Mi
Keyword(s):  
Surface Tension ◽  
Half Space ◽  
Surface Elasticity ◽  
Elastic Half Space ◽  
Indentation Hardness ◽  
Bending Rigidity ◽  
Size Dependent ◽  
Significant Difference ◽  
Nanoindentation Hardness ◽  
Membrane Stiffness

Previous studies demonstrate that, for nanostructures under transverse bending, the effective Young modulus is appreciably greater (in magnitude) than that of the same elements under axial loads. Therefore, in addition to the conventional residual surface tension and membrane stiffness, the curvature dependence of surface energy is desired for inhomogeneously strained nanostructures. In this paper, we aim to reevaluate the size-dependent nanoindentation hardness of an elastic half-space subjected to nanosized frictionless traction, through the use of both the curvature-independent Gurtin–Murdoch and the curvature-dependent Steigmann–Ogden models of surface elasticity. The nanoindentation problem is solved by the integration of Boussinesq’s method of displacement potentials and Hankel integral transforms. As examples, the effects of residual surface tension, membrane stiffness, and bending rigidity of the half-space boundary are parametrically analyzed in detail for a uniform circular pressure and a concentrated normal force. The observations in semianalytical calculations suggest a significant difference in the nanoindentation hardnesses predicted from the two popular models of surface mechanics. In most cases, the inclusion of bending rigidity results in smaller displacements and stresses, and therefore higher indentation hardness. Based on physically interpretable numerical values of surface material properties, we show that a curvature-dependent model of surface elasticity is required in order to characterize the size-dependent feature of nanoindentation problems correctly.

Contact Analysis Using Surface Green’s Functions for Isotropic Materials With Surface Stress and Surface Elasticity

2010 ◽  
Author(s):  
Hideo Koguchi ◽  
Naoki Nishi
Keyword(s):  
Green Function ◽  
Green’S Function ◽  
Amorphous Silicon ◽  
Green's Function ◽  
Surface Stress ◽  
Surface Elasticity ◽  
Contact Analysis ◽  
Isotropic Materials ◽  
Stroh's Formalism ◽  
Stroh’S Formalism

Surface stress and surface elasticity are related to an organization of surface pattern and reconstruction of surface atoms. When the size of material reduces to a nanometer level, a ratio of surface to volume increases. Then, surface stress and surface elasticity influence on mechanical response near surface for an external force on the surface. Stroh formalism is very useful for analyzing the stress and displacement in anisotropic materials. When the Stroh’s formalism is applied to isotropic materials, the eigen matrix derived from equilibrium equation yields a triple root of i (i: imaginary unit), and then an independent eigen vector corresponding to the eigen value can not be determined. In this paper, surface Green function for isotropic materials is derived using Stroh’s formalism. The derived Green function considering neither surface stress nor surface elasticity agrees with the solution of Boussinesq. The surface Green’s function considering surface stress and surface elasticity is used for analyzing the displacement fields in amorphous silicon. It was found that the displacements obtained from the Green’s function were less than those from Boussinesq’s solution. Furthermore, the derived surface Green’s function is applied to a contact analysis for isotropic materials such as amorphous silicon. It is found that an apparent Young’s modulus determined from a force-indentation depth curve increases when surface stress and elasticity is taken into account in the analysis.

scholarly journals Elastic Analysis for Nanocontact Problem with Surface Stress Effects under Shear Load

2012 ◽  
Vol 2012 ◽  
pp. 1-7 ◽  
Author(s):  
D. X. Lei ◽  
L. Y. Wang ◽  
Z. Y. Ou
Keyword(s):  
Surface Stress ◽  
Solid Mechanics ◽  
Integral Transform ◽  
Surface Elasticity ◽  
Elastic Field ◽  
Fourier Integral ◽  
Shear Load ◽  
Transform Method ◽  
Stress Effects ◽  
Special Cases

Consideration of surface stress effects on the elastic field of nanocontact problem has extensive applications in several modern problems of solid mechanics. In this paper, the effects of surface stress on the contact problem at nanometers are studied in the frame of surface elasticity theory. Fourier integral transform method is adopted to derive the fundamental solution of the nanocontact problem under shear load. As two special cases, the deformations induced by a uniformly distributed shear load and a concentrated shear force are discussed in detail, respectively. The results indicate some interesting characteristics in nanocontact mechanics, which are distinctly different from those in macrocontact problem. At nanoscale, both the contact stresses and the displacements on the deformed surface transit continuously across the uniform distributed shear load boundary as a result of surface stress. In addition, the indent depth and the contact stress depend strongly on the surface stress for nanoindentation.

Research on the Relationship between Indenter Tip Radius and Hardness with a Self-Designed Nanohardness Test Device

2008 ◽  
Vol 392-394 ◽  
pp. 267-270
Author(s):  
Qiang Liu ◽  
Ying Xue Yao ◽  
L. Zhou
Keyword(s):  
Single Crystal ◽  
Indentation Depth ◽  
Single Crystal Silicon ◽  
Indentation Hardness ◽  
Displacement Curve ◽  
Test Device ◽  
Crystal Silicon ◽  
Load Displacement ◽  
Depth Sensitivity ◽  
Tip Radius

Nanoindentation device has the ability to make the load-displacement measurement with sub-nanometer indentation depth sensitivity, and the nanohardness of the material can be achieved by the load-displacement curve. Aiming at the influence law of indenter tip radius to indentation hardness, testing on the hardness of single-crystal silicon were carried out with the new self-designed nanohardness test device based on nanoindentation technique. Two kinds of Berkovich indenter with radius 40nm and 60nm separately were used in this experiment. According to the load-depth curve, the hardness of single-crystal silicon was achieved by Oliver-Pharr method. Experimental results are presented which show that indenter tip radius do influence the hardness, the hardness value increases and the indentation size effect (ISE) becomes obvious with the increasing of tip radius under same indentation depth.

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