Indentation load–depth relation for an elastic layer with surface tension

Li, Shaoheng; Yuan, Weike; Ding, Yue; Wang, Gangfeng

doi:10.1177/1081286518774090

Cited by 9 publications

(3 citation statements)

References 35 publications

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“…Several theoretical and experimental results have demonstrated the essential roles of size effect and surface effect on contact behavior when the indentation depth or punch size of materials are at the micro-/nano-scale [12][13][14]. In particular, due to the increasing ratio of the surface to bulk volume of materials at the nano-scale, the surface effect on nanocontact behavior played a dominant role [15,16]. Gurtin and Murdoch [17] first built surface elasticity theory to describe the surface effect of elastic materials.…”

Section: Introductionmentioning

confidence: 99%

Surface effects on elastohydrodynamic lubrication contact of piezoelectric materials with non-Newtonian fluid

Su,

Song,

2023

Smart Mater. Struct.

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By using surface piezoelectricity theory, this article investigates the elastohydrodynamic lubrication (EHL) line contact of a transversely isotropic piezoelectric half-plane with consideration of the surface effect under a rigid cylindrical punch. The surface effect in the surface piezoelectricity theory is mainly described by the following parameters: surface piezoelectric constant, surface dielectric constant, surface elastic constant, and residual surface stress. The punch is treated as the electrical insulator. The lubricant, whose viscosity and density are dependent on fluid pressure, is chosen as non-Newtonian fluid. Firstly, by analyzing the frictionless dry contact of piezoelectric materials with surface effect, dry contact pressure distribution and EHL film thickness equation are obtained. Then, an iterative method is proposed to get fluid pressure and film thickness at lubricant contact region by calculating the fluid-solid coupled nonlinear equations. Effects of surface dielectric constant, surface piezoelectric constant, surface elastic constant, residual surface stress, punch radius, entraining velocity, and slide/roll ratio on the film thickness and fluid pressure are examined. Our analysis indicates that surface effect has an essential effect on the EHL contact behaviors of piezoelectric materials at micro-/nano-scales.

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Section: Introductionmentioning

confidence: 99%

Surface effects on elastohydrodynamic lubrication contact of piezoelectric materials with non-Newtonian fluid

Su,

Song,

2023

Smart Mater. Struct.

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“…For nanoindentation with the indentation depth on the order of nanometers, the surface mechanics should be required to analyze the indentation test. Owing to the large specific surface area of materials at micro-/ nano-scale, the surface dependence of materials has been well recognized in recent years (Dingreville et al, 2005;Li et al, 2019;Wong et al, 1997). In particular, both atomistic simulations and experiments strongly revealed that surface effect played an essential role in contact problems for the indentation depths less than 100 nanometers (Mohammadi and Sharma, 2012;Wang and Feng, 2007).…”

Section: Introductionmentioning

confidence: 99%

Axisymmetric contact analysis of piezoelectric materials with surface effect

Hong-xia

2021

Journal of Intelligent Material Systems and Structures

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Based on the surface piezoelectricity theory, this article predicts the axisymmetric smooth contact of a piezoelectric half-space indented by a rigid insulated punch. In this theory, the surface effect is characterized with four material parameters: the surface elastic constant, surface residual stress, surface piezoelectric constant and surface dielectric constant. By applying Hankel integral transform, the fundamental solution for this axisymmetric contact problem is derived with the surface effect. Then, the normal contact stress, radial electric displacement and radial stress of the contact surface are solved numerically. Finally, the surface effects on the normal contact stress, radial electric displacement and radial stress are analyzed. It is found that the surface effect is a significant influencing factor on the axisymmetric contact behaviors of micro-/nano-scale piezoelectric materials.

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“…Li et al (2019a) investigated the contact between a conical asperity and a rough surface possessing surface tension. Based on parametric studies, Li et al (2019b) developed empirical expressions of indentation load-depth and load-contact radius relations for an elastic layer with surface tension.…”

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confidence: 99%

Nanoindentation of a half-space due to a rigid cylindrical roller based on Steigmann–Ogden surface mechanical model

2020

Int J Mech Mater Des

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In this article, a semianalytical method of solution is developed for the nanocontact problem of elastic half-space indented by a rigid cylindrical roller. The mechanical formulation is based on the complete version of Steigmann-Ogden surface elasticity theory. Surface tension, surface tensile stiffness and surface flexural rigidity of the half-space boundary are all taken into consideration. Fourier integral transform method converts the governing equations and displacement boundary conditions of the nanocontact problem into a singular integral equation. Gauss-Chebyshev quadrature and an iterative algorithm numerically solve this integral equation and the force equilibrium condition. The developed semianalytical solution is general in the sense that it can reduce to a few simplified theories. These include classical solution, considering only a single surface material parameter, and Gurtin-Murdoch surface elasticity theory, for which analytical kernel functions of the singular integral equation are presented. Dimension analysis demonstrates that the effects of Steigmann-Ogden surface elasticity on the two-dimensional Hertzian nanocontact properties are up to three dimensionless ratios among surface material parameters, shear modulus and the size of nanocontact. Moreover, least-squares regression analysis suggests that, in the presence of surface effects, an elliptic arc less than a half can represent the nanocontact pressure. When compared with their classical counterparts, lower maximum contact pressure and nonzero minimum pressure are found. Parametric experiments further show that surface tension and surface flexural rigidity significantly affect contact length, contact pressure, contact stiffness as well as displacements and stresses near the half-space boundary. In contrast, the effects of surface membrane stiffness are of secondary importance. In general, smaller indenters and larger surface constants lead to higher loadcarrying capabilities of half-space and thus better mechanical responses. Keywords Surface flexural rigidity Á Membrane stiffness Á Surface tension Á Singular integral equation Á Hertzian contact 1 Introduction Both experimental observations and theoretical analysis have demonstrated the significant influence of surface mechanics and physics on the mechanical

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Indentation load–depth relation for an elastic layer with surface tension

Cited by 9 publications

References 35 publications

Surface effects on elastohydrodynamic lubrication contact of piezoelectric materials with non-Newtonian fluid

Surface effects on elastohydrodynamic lubrication contact of piezoelectric materials with non-Newtonian fluid

Axisymmetric contact analysis of piezoelectric materials with surface effect

Nanoindentation of a half-space due to a rigid cylindrical roller based on Steigmann–Ogden surface mechanical model

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