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Mohamed Belhaq - One of the best experts on this subject based on the ideXlab platform.

  • Contact Stiffness modulation in Contact mode atomic force microscopy
    International Journal of Non-linear Mechanics, 2013
    Co-Authors: Ilham Kirrou, Mohamed Belhaq
    Abstract:

    Abstract The effect of fast Contact Stiffness modulation on the frequency response in Contact-mode atomic force microscopy is studied analytically near primary resonance. Based on the Hertzian Contact theory, a lumped single degree of freedom oscillator is considered for modeling the Contact-mode dynamics between the tip of the microbeam and the sample. Averaging method and perturbation analysis are performed to obtain the modulation equations of the slow dynamic. The influence of the Contact Stiffness modulation on the non-linear characteristic of the frequency response is examined. We find that the amplitude of the Contact Stiffness modulation influences significantly the amplitude of the tip oscillation as well as the shift direction of the frequency response indicating that such a modulation can be used to characterize the local elastic properties of the sample. Comparison between the analytical predictions and the numerical simulations is given and application to a real atomic force microscope example is provided.

  • effect of Contact Stiffness modulation in Contact mode afm under subharmonic excitation
    Communications in Nonlinear Science and Numerical Simulation, 2013
    Co-Authors: Ilham Kirrou, Mohamed Belhaq
    Abstract:

    We report on the effect of fast Contact Stiffness modulation on frequency response to 2:1 subharmonic resonance in Contact-mode atomic force microscopy. The model of the Contact-mode dynamic between the tip of the microbeam and the moving surface consists of a lumped single degree of freedom Hertzian Contact oscillator. Perturbation methods are applied to obtain the frequency response of the slow dynamic of the system. We focus on the effect of the amplitude and the frequency of the modulation on the nonlinear characteristic of the Contact Stiffness, the jump phenomenon and the shift in the frequency response of the subharmonic. We also show the effect of the Contact Stiffness modulation on the interval of the unstable trivial solution which is directly correlated to the depth of the jump. The obtained results can directly influence the material properties and the loss of Contact between the tip and the sample.

  • frequency shift and hysteresis suppression in Contact mode afm using Contact Stiffness modulation
    MATEC Web of Conferences, 2012
    Co-Authors: Ilham Kirrou, Mohamed Belhaq
    Abstract:

    In this paper the frequency response shift and hysteresis suppression of Contact-mode atomic force microscopy is investigated using parametric modulation of the Contact Stiffness. Based on the Hertzian Contact theory, a lumped single degree of freedom oscillator is considered for modeling the cantilever dynamics Contact- mode atomic force microscopy. We use the technique of direct partition of motion and the method of multiple scales to obtain, respectively, the slow dynamic and the corresponding slow flow of the system. As results, this study shows that the amplitude of the Contact Stiffness modulation has a significant effect on the frequency response. Specifically, increasing the amplitude of the Stiffness modulation suppresses hysteresis, decreases the peak amplitude and produces shifts towards higher and lower frequencies.

G M Pharr - One of the best experts on this subject based on the ideXlab platform.

  • measuring poisson s ratio during nanoindentation via lateral Contact Stiffness issues of slip and plasticity
    arXiv: Materials Science, 2021
    Co-Authors: Owen Brazil, G M Pharr
    Abstract:

    Although Poisson's ratio, v, is a quantity of great importance in materials design, presently, very few methods are available to measure it at small (micrometre) scales and those typically involve intensive geometric refinement of the sample. In this work we show how Poisson's ratio may be measured during nanoindentation experiments by means of a second load actuator oriented orthogonally to the primary vertical load axis. We apply a small oscillating lateral load to Berkovich and sphero-conical indenter tips during nanoindentation into fused silica and metallic samples. This enables the elastic lateral Contact Stiffness to be measured as a function of depth in a manner analogous to continuous Stiffness measurements in conventional indentation experiments. The Stiffness may in turn be used to calculate v. During constant strain rate experiments, we extract values of v = 0.16 for fused silica and v = 0.34 for polycrystalline aluminium over indentation depths of several hundred nanometres. We highlight two critical issues that must be addressed to ensure accurate measurement of v during indentation; partial slip and additional plasticity brought about through the added shear under tangential loading. We study these separate phenomena in fused silica and single crystal nickel, suggesting that interfacial slip is favoured in harder, brittle materials, while plasticity is dominant in more ductile materials. We offer some suggestions on how to mitigate these problems based on tip geometry and loading protocols.

  • nanoscale incipient asperity sliding and interface micro slip assessed by the measurement of tangential Contact Stiffness
    Scripta Materialia, 2006
    Co-Authors: B N Lucas, G M Pharr, W C Oliver
    Abstract:

    Experiments with a multidimensional nano-Contact system have shown that, prior to kinetic frictional sliding, there is a significant reduction of the tangential Contact Stiffness relative to the elastic prediction. The reduction occurs at Contact sizes below about 50–200 nm for aluminum single crystals and several other materials. Using a cohesive interface model, we find that this reduction corresponds to a transition from a small-scale-slip to large-scale-slip condition of the interface.

  • on the generality of the relationship among Contact Stiffness Contact area and elastic modulus during indentation
    Journal of Materials Research, 1992
    Co-Authors: G M Pharr, W C Oliver, F R Brotzen
    Abstract:

    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 between 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.

Ilham Kirrou - One of the best experts on this subject based on the ideXlab platform.

  • Contact Stiffness modulation in Contact mode atomic force microscopy
    International Journal of Non-linear Mechanics, 2013
    Co-Authors: Ilham Kirrou, Mohamed Belhaq
    Abstract:

    Abstract The effect of fast Contact Stiffness modulation on the frequency response in Contact-mode atomic force microscopy is studied analytically near primary resonance. Based on the Hertzian Contact theory, a lumped single degree of freedom oscillator is considered for modeling the Contact-mode dynamics between the tip of the microbeam and the sample. Averaging method and perturbation analysis are performed to obtain the modulation equations of the slow dynamic. The influence of the Contact Stiffness modulation on the non-linear characteristic of the frequency response is examined. We find that the amplitude of the Contact Stiffness modulation influences significantly the amplitude of the tip oscillation as well as the shift direction of the frequency response indicating that such a modulation can be used to characterize the local elastic properties of the sample. Comparison between the analytical predictions and the numerical simulations is given and application to a real atomic force microscope example is provided.

  • effect of Contact Stiffness modulation in Contact mode afm under subharmonic excitation
    Communications in Nonlinear Science and Numerical Simulation, 2013
    Co-Authors: Ilham Kirrou, Mohamed Belhaq
    Abstract:

    We report on the effect of fast Contact Stiffness modulation on frequency response to 2:1 subharmonic resonance in Contact-mode atomic force microscopy. The model of the Contact-mode dynamic between the tip of the microbeam and the moving surface consists of a lumped single degree of freedom Hertzian Contact oscillator. Perturbation methods are applied to obtain the frequency response of the slow dynamic of the system. We focus on the effect of the amplitude and the frequency of the modulation on the nonlinear characteristic of the Contact Stiffness, the jump phenomenon and the shift in the frequency response of the subharmonic. We also show the effect of the Contact Stiffness modulation on the interval of the unstable trivial solution which is directly correlated to the depth of the jump. The obtained results can directly influence the material properties and the loss of Contact between the tip and the sample.

  • frequency shift and hysteresis suppression in Contact mode afm using Contact Stiffness modulation
    MATEC Web of Conferences, 2012
    Co-Authors: Ilham Kirrou, Mohamed Belhaq
    Abstract:

    In this paper the frequency response shift and hysteresis suppression of Contact-mode atomic force microscopy is investigated using parametric modulation of the Contact Stiffness. Based on the Hertzian Contact theory, a lumped single degree of freedom oscillator is considered for modeling the cantilever dynamics Contact- mode atomic force microscopy. We use the technique of direct partition of motion and the method of multiple scales to obtain, respectively, the slow dynamic and the corresponding slow flow of the system. As results, this study shows that the amplitude of the Contact Stiffness modulation has a significant effect on the frequency response. Specifically, increasing the amplitude of the Stiffness modulation suppresses hysteresis, decreases the peak amplitude and produces shifts towards higher and lower frequencies.

Qi Chen - One of the best experts on this subject based on the ideXlab platform.

  • research on normal Contact Stiffness of rough surface considering friction based on fractal theory
    Applied Surface Science, 2015
    Co-Authors: Peng Liu, Han Zhao, Kang Huang, Qi Chen
    Abstract:

    Abstract The friction which plays an essential role on normal Contact Stiffness is usually omitted in existed researches, thus a modified fractal model for normal Contact Stiffness considering friction is discussed in this paper for calculating normal Contact Stiffness precisely and reasonably. The model is obtained by introducing a specific coefficient factor into the equation of the normal Contact Stiffness which is deduced by employing the theory of fractal Contact and the definition of Stiffness. Through the simulation and comparison with the original model and experiment result, it is clearly concluded that the modified model can reveal the influence of friction on Contact area as well as calculate the normal Contact Stiffness more accurately. Furthermore, the numerical results show that the normal Contact Stiffness increases with the normal load; it is advantageous to improve the normal Contact Stiffness of rough surface by adding fractal dimension-D and reducing fractal scaling parameter-G. Also, the friction coefficient decreases with adding D and G and the fractal dimension has a marked impact on the friction coefficient. The presented achievements will help to analyze the performance for surface Contact dynamics in the future.

Yunyun Sun - One of the best experts on this subject based on the ideXlab platform.

  • fractal modeling of normal Contact Stiffness for rough surface Contact considering the elastic plastic deformation
    Journal of The Brazilian Society of Mechanical Sciences and Engineering, 2019
    Co-Authors: Huifang Xiao, Yunyun Sun, Zaigang Chen
    Abstract:

    In this work, a new formulation of elastic–plastic Contact model for the normal Contact between rough surfaces is proposed based on the fractal theory. The surface topography is described using the modified one-variable Weierstrass–Mandelbrot fractal function. A new elastoplastic asperity Contact model is developed based on the Contact mechanics combined with the continuity and smoothness of mean Contact pressure and Contact load across different deformation regimes from elastic to elastoplastic, and from elastoplastic to fully plastic. The Contact Stiffness of a single asperity in the three deformation regimes of fully plastic, elastoplastic and elastic is derived, which changes smoothly at transit points between different deformation modes and overcomes the shortcoming of discontinuity derived from previous model. The Contact Stiffness and Contact load of the whole surface in the three deformation regimes are formulated by integrating the micro-asperity Contact. The difference between Contact Stiffness calculated from the plastic–elastoplastic–elastic three Contact regimes and plastic–elastic two Contact regimes is not obvious for surface with rougher topograph; however, for surface with smoother topograph, the two Contact regimes predict a much smaller Contact Stiffness. The relationship of the normal Contact Stiffness and the normal Contact force follows a power law function for the fractal surface Contact considering three deformation regimes. The power exponent is nonlinearly dependent on the fractal dimension, which is different from the linear relationship for the purely elastic Contact.

  • On the normal Contact Stiffness and Contact resonance frequency of rough surface Contact based on asperity micro-Contact statistical models
    European Journal of Mechanics - A Solids, 2019
    Co-Authors: Huifang Xiao, Yunyun Sun
    Abstract:

    Abstract Contact Stiffness is an important parameter for describing the interface characteristics in many engineering applications. In this paper, five different statistical micro-models including the Greenwood-Williamson (GW), Zhao-Maietta-Chang (ZMC), Kogut-Etsion (KE), Jackson-Green (JG) and Brake are employed to predict the normal Contact Stiffness for rough surface Contact. It is found that the expressions of Contact Stiffness obtained using the statistical micro-models are very complex and the direct relationship between the Contact Stiffness and normal load is not available. Accordingly, an explicit approximated expression for Contact Stiffness is established in terms of normal load based on the results of numerical simulations. The normal Contact Stiffness as a function of normal load can be approximated using a power law, in which the coefficient and power are related to surface roughness parameters, material properties as well as nominal Contact area. The close agreement between the predicted results and full numerical simulations verify the accuracy of the established explicit expression. The Contact Stiffness calculated using the predictive expressions are also compared with available experimental results from both ultrasonic method and Contact resonance method. Further, the explicit expression of Contact resonance frequency for rough surface Contact with respect to the normal load is also provided, which can be used to evaluate the Contact resonance frequency. The predicted Contact resonance frequency is also validated through comparing with experimental results.

  • an improved virtual material based acoustic model for Contact Stiffness measurement of rough interface using ultrasound technique
    International Journal of Solids and Structures, 2018
    Co-Authors: Huifang Xiao, Yunyun Sun
    Abstract:

    Abstract In this work, an improved acoustic model based on virtual material is proposed to provide an accurate measurement of interfacial Contact Stiffness using ultrasound. The rough interface is assumed to be a thin layer of virtual material to incorporate the effect of ultrasound attenuation at the interface. The derived acoustic model shows that the developed Contact Stiffness expression is a refinement of the general spring model by considering the interfacial property and is related to the material properties of the virtual material thin layer. The analytical solutions of the material parameters for the virtual material are further deduced based on the statistical micro-Contact theory. It reveals that the surface roughness parameters of the Contact interface and the material property of the Contact body are other information required to improve the measurement accuracy of Contact Stiffness, in addition to the ultrasonic measurement parameters in the original spring model. The accuracy of the developed acoustic model for Contact Stiffness measurement is verified by comparison with the spring model and the statistical Contact models.

  • investigation into the normal Contact Stiffness of rough surface in line Contact mixed elastohydrodynamic lubrication
    Tribology Transactions, 2018
    Co-Authors: Huifang Xiao, Yunyun Sun
    Abstract:

    In this work, the statistical asperity microContact models in combination with the acoustic spring model and the load sharing concept are utilized to study the interfacial normal Contact Stiffness ...