Nanoindentation Method for Determining the Initial Contact and Adhesion Characteristics of Soft Polydimethylsiloxane

2005 ◽  
Vol 20 (8) ◽  
pp. 2004-2011 ◽  
Author(s):  
Yifang Cao ◽  
Dehua Yang ◽  
Wole Soboyejoy
Keyword(s):  
Indentation Depth ◽  
Contact Point ◽  
Nonlinear Least Squares ◽  
Soft Materials ◽  
Work Of Adhesion ◽  
Contact Radius ◽  
Initial Contact ◽  
Combined Use ◽  
Fitting In ◽  
Load Indentation

In this paper, we present a method for determining the initial contact point and nanoindentation load–indentation depth characteristics for soft materials. The method is applied to the prediction of the load–indentation depth characteristics of polydimethylsiloxane. It involves the combined use of Johnson–Kendall–Roberts and Maugis–Dugdale adhesion theories and nonlinear least squares fitting in the determination of the initial contact point, the transition parameter, and the contact radius at zero contact load. The elastic modulus and the work of adhesion are also extracted from the load–indentation depth curves.

scholarly journals Adhesion Hysteresis Due to Chemical Heterogeneity

2020 ◽  
pp. 473-483
Author(s):  
Valentin L. Popov
Keyword(s):  
Surface Energy ◽  
Specific Surface ◽  
Spatial Dependence ◽  
Indentation Depth ◽  
Chemical Mechanism ◽  
Work Of Adhesion ◽  
Chemical Heterogeneity ◽  
Initial Contact ◽  
Specific Work ◽  
Surface Energies

AbstractAccording the JKR theory of adhesivecontact, changes of the contact configuration after formation of the adhesive neck and before detaching are completely reversible. This means, that after formation of the initial contact, the force-distance dependencies should coincide, independently of the direction of the process (indentation or pull-off). In the majority of real systems, this invariance is not observed. The reasons for this may be either plastic deformation in the contacting bodies or surface roughness. One further mechanism of irreversibility (and corresponding energy dissipation) may be chemical heterogeneity of the contact interface leading to the spatial dependence of the specific work of adhesion. In the present paper, this “chemical” mechanism is analyzed on a simple example of an axisymmetric contact (with axisymmetric heterogeneity). It is shown that in the asymptotic case of a “microscopic heterogeneity”, the system follows, during both indentation and pull-off, JKR curves, however, corresponding to different specific surface energies. After the turning point of the movement, the contact area first does not change and the transition from one JKR curve to the other occurs via a linear dependency of the force on indentation depth. The macroscopic behavior is not sensitive to the absolute and relative widths of the regions with different surface energy but depends mainly on the values of the specific surface energy.

A simplified formulation of adhesion problems with elastic plates

2009 ◽  
Vol 465 (2107) ◽  
pp. 2217-2230 ◽  
Author(s):  
Carmel Majidi ◽  
George G. Adams
Keyword(s):  
Potential Energy ◽  
Contact Area ◽  
Contact Region ◽  
Bending Moment ◽  
Total Potential Energy ◽  
Work Of Adhesion ◽  
Contact Radius ◽  
Algebraic Complexity ◽  
Elastic Plates ◽  
Total Potential

The solution of adhesion problems with elastic plates generally involves solving a boundary-value problem with an assumed contact area. The contact region is then found by minimizing the total potential energy with respect to the contact area (i.e. the contact radius for the axisymmetric case). Such a procedure can be extremely long and tedious. Here, we show that the inclusion of adhesion is equivalent to specifying a discontinuous internal bending moment at the contact region boundary. The magnitude of this moment discontinuity is related to the work of adhesion and flexural rigidity of the plate. Such a formulation can greatly reduce the algebraic complexity of solving these problems. It is noted that the related plate contact problems without adhesion can also be solved by minimizing the total potential energy. However, it has long been recognized that it is mathematically more efficient to find the contact area by specifying a continuous internal bending moment at the boundary of the contact region. Thus, our moment discontinuity method can be considered to be a generalization of that procedure which is applicable for problems with adhesion.

Spatial Kinematic Analysis of Threaded Fastener Assembly

2005 ◽  
Vol 128 (1) ◽  
pp. 116-127 ◽  
Author(s):  
Stephen Wiedmann ◽  
Bob Sturges
Keyword(s):  
Design Space ◽  
Compliant Mechanisms ◽  
Contact Point ◽  
Three Dimensional ◽  
Vertical Movement ◽  
Initial Contact ◽  
Geometric Problem ◽  
Intelligent Sensor ◽  
Contact State ◽  
Contact Points

Compliant mechanisms for rigid part mating exist for prismatic geometries. A few instances are known of mechanisms to assemble screw threads. A comprehensive solution to this essentially geometric problem comprises at least three parts: parametric equations for nut and bolt contact in the critical starting phase of assembly, the possible space of motions between these parts during this phase, and the design space of compliant devices which accomplish the desired motions in the presence of friction and positional uncertainty. This work concentrates on the second part in which the threaded pair is modeled numerically, and contact tests are automated through software. Tessellated solid models were used during three-dimensional collision analysis to enumerate the approximate location of the initial contact point. The advent of a second contact point presented a more constrained contact state. Thus, the bolt is rotated about a vector defined by the initial two contact points until a third contact location was found. By analyzing the depth of intersection of the bolt into the nut as well as the vertical movement of the origin of the bolt reference frame, we determined that there are three types of contacts states present: unstable two-point, quasi-stable two-point, stable three point. The space of possible motions is bounded by these end conditions which will differ in detail depending upon the starting orientations. We investigated all potential orientations which obtain from a discretization of the roll, pitch, and yaw uncertainties, each of which has its own set of contact points. From this exhaustive examination, a full contact state history was determined, which lays the foundation for the design space of either compliant mechanisms or intelligent sensor-rich controls.

AN APPROXIMATE FORMULATION OF THE EFFECTIVE INDENTATION MODULUS OF ELASTICALLY ANISOTROPIC FILM-ON-SUBSTRATE SYSTEMS

2009 ◽  
Vol 01 (03) ◽  
pp. 515-525 ◽  
Author(s):  
T. L. LI ◽  
J. H. LEE ◽  
Y. F. GAO
Keyword(s):  
Applied Load ◽  
Indentation Depth ◽  
Surface Displacement ◽  
Contact Radius ◽  
Radial Coordinate ◽  
Indentation Modulus ◽  
Approximate Formulation ◽  
Punch Contact ◽  
Indenter Shape ◽  
Circular Contact

Frictionless contact between an arbitrarily-shaped rigid indenter and an elastically anisotropic film-on-substrate system can be regarded as being superposed incrementally by a flat-ended punch contact, the shape and size of which are determined by the indenter shape, indentation depth (or applied load) and elastic properties of film and substrate. For typical nanoindentation applications, the indentation modulus can thus be approximated from the response of a circular contact with pressure of the form of [1 - (r/a)2]-1/2, where r is the radial coordinate and a is the contact radius. The surface-displacement Green's function for elastically anisotropic film-on-substrate system is derived in closed-form by using the Stroh formalism and the two-dimensional Fourier transform. The predicted dependence of the effective modulus on the ratio of film thickness to contact radius agrees well with detailed finite element simulations. Implications in evaluating film modulus by nanoindentation technique are also discussed.

Nonlinear least-squares data fitting in Excel spreadsheets

2010 ◽  
Vol 5 (2) ◽  
pp. 267-281 ◽  
Author(s):  
Gerdi Kemmer ◽  
Sandro Keller
Keyword(s):  
Least Squares ◽  
Nonlinear Least Squares ◽  
Data Fitting ◽  
Fitting In

A Model of a Trapped Particle Under a Plate Adhering to a Rigid Surface

2013 ◽  
Vol 80 (5) ◽  
Author(s):  
Joel R. Parent ◽  
George G. Adams
Keyword(s):  
Numerical Solution ◽  
Large Deflection ◽  
Nonlinear Differential Equations ◽  
Plate Thickness ◽  
Work Of Adhesion ◽  
Contact Radius ◽  
Approximate Analytic Solution ◽  
Total Potential ◽  
Curve Fit ◽  
Deflection Theory

Micro and nanomechanics are growing fields in the semiconductor and related industries. Consequently obstacles, such as particles trapped between layers, are becoming more important and warrant further attention. In this paper a numerical solution to the von Kármán equations for moderately large deflection is used to model a plate deformed due to a trapped particle lying between it and a rigid substrate. Due to the small scales involved, the effect of adhesion is included. The recently developed moment-discontinuity method is used to relate the work of adhesion to the contact radius without the explicit need to calculate the total potential energy. Three different boundary conditions are considered—the full clamp, the partial clamp, and the compliant clamp. Curve-fit equations are found for the numerical solution to the nondimensional coupled nonlinear differential equations for moderately large deflection of an axisymmetric plate. These results are found to match the small deflection theory when the deflection is less than the plate thickness. When the maximum deflection is much greater than the plate thickness, these results represent the membrane theory for which an approximate analytic solution exists.

scholarly journals Determination of the optimum ball radius for researching materials using ball indenting

2021 ◽  
Vol 5 (4) ◽  
pp. 227-232
Author(s):  
N. N. Avtonomov ◽  
A. V. Tololo
Keyword(s):  
Indentation Depth ◽  
Sample Material ◽  
Axial Deformation ◽  
Obvious Change ◽  
Actual Depth ◽  
Element Method ◽  
Load Indentation

The article discusses the study of the effect of a change in the radius of the ball in the injecting of the sample on the curve in the coordinates «load – indentation depth», the deviation of the indentation depth during elastoplastic indentation from the indentation depth with the elastic indentation and the amount of the axial deformation of the ball. The study was conducted using the Ansys Mechanical APDL program implementing the fenite element method. In the process of the study, it was found that with a change in the radius of the ball, there is no obvious change in the behavior of the sample material, and the deviation of the indentation depth during the elastoplastic indulgence from the indentation depth during the elastic indentation is not dependent on the size of the ball radius. There was also an effect of changing the radius of the ball on the size of the axial deformation of the ball and proposed a formula for determining the size of the axial deformation of the ball for the ball of any diameter, which will determine the actual depth of the ball into the ball when using the balls of different radius.

scholarly journals Calibration of a Constitutive Model from Tension and Nanoindentation for Lead-Free Solder

Micromachines ◽  
2018 ◽  
Vol 9 (11) ◽  
pp. 608 ◽  
Author(s):  
Xu Long ◽  
Xiaodi Zhang ◽  
Wenbin Tang ◽  
Shaobin Wang ◽  
Yihui Feng ◽  
...  
Keyword(s):  
Integrated Circuits ◽  
Penetration Depth ◽  
Applied Load ◽  
Indentation Depth ◽  
Lead Free ◽  
Constitutive Behaviour ◽  
Sac305 Solder ◽  
Stress Strain ◽  
Significant Difference ◽  
Load Indentation

It is challenging to evaluate constitutive behaviour by using conventional uniaxial tests for materials with limited sizes, considering the miniaturization trend of integrated circuits in electronic devices. An instrumented nanoindentation approach is appealing to obtain local properties as the function of penetration depth. In this paper, both conventional tensile and nanoindentation experiments are performed on samples of a lead-free Sn–3.0Ag–0.5Cu (SAC305) solder alloy. In order to align the material behaviour, thermal treatments were performed at different temperatures and durations for all specimens, for both tensile experiments and nanoindentation experiments. Based on the self-similarity of the used Berkovich indenter, a power-law model is adopted to describe the stress–strain relationship by means of analytical dimensionless analysis on the applied load-penetration depth responses from nanoindentation experiments. In light of the significant difference of applied strain rates in the tensile and nanoindentation experiments, two “rate factors” are proposed by multiplying the representative stress and stress exponent in the adopted analytical model, and the corresponding values are determined for the best predictions of nanoindentation responses in the form of an applied load–indentation depth relationship. Eventually, good agreement is achieved when comparing the stress–strain responses measured from tensile experiments and estimated from the applied load–indentation depth responses of nanoindentation experiments. The rate factors ψ σ and ψ n are calibrated to be about 0.52 and 0.10, respectively, which facilitate the conversion of constitutive behaviour from nanoindentation experiments for material sample with a limited size.

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