Determination of Poisson’s Ratio by Spherical Indentation Using Neural Networks—Part I: Theory

2000 ◽  
Vol 68 (2) ◽  
pp. 218-223 ◽  
Author(s):  
N. Huber ◽  
A. Konstantinidis ◽  
Ch. Tsakmakis
Keyword(s):  
Poisson Ratio ◽  
Indentation Test ◽  
Inverse Function ◽  
Elastic Half Space ◽  
Spherical Indentation ◽  
Isotropic Hardening ◽  
Plastic Yield ◽  
Load Response ◽  
Reduced Modulus

When studying analytically the penetration of an indenter of revolution into an elastic half-space use is commonly made of the fraction Er=E/1−ν2. Because of this, only Er is determined from the indentation test, while the value of ν is usually assumed. However, as shown in the paper, if plastic deformation is involved during loading, the depth-load trajectory depends on the reduced modulus and, additionally, on the Poisson ratio explicitly. The aim of the paper is to show, with reference to a simple plasticity model exhibiting linear isotropic hardening, that the Poisson ratio can be determined uniquely from spherical indentation if the onset of plastic yield is known. To this end, a loading and at least two unloadings in the plastic regime have to be considered. Using finite element simulations, the relation between the material parameters and the quantities characterizing the depth-load response is calculated pointwise. An approximate inverse function represented by a neural network is derived on the basis of these data.

Determination of Poisson’s Ratio by Spherical Indentation Using Neural Networks—Part II: Identification Method

2000 ◽  
Vol 68 (2) ◽  
pp. 224-229 ◽  
Author(s):  
N. Huber ◽  
Ch. Tsakmakis
Keyword(s):  
Neural Networks ◽  
Poisson’S Ratio ◽  
Inverse Function ◽  
Poisson's Ratio ◽  
Spherical Indentation ◽  
Plastic Yield ◽  
Different Depths ◽  
Unloading Stiffness ◽  
First Time

In a previous paper it has been shown that the load and the unloading stiffness are, among others, explicit functions of the Poisson’s ratio, if a spherical indenter is pressed into a metal material. These functions can be inverted by using neural networks in order to determine the Poisson’s ratio as a function of the load and the unloading stiffness measured at different depths. Also, the inverse function possesses as an argument the ratio of the penetration depth and that depth, at which plastic yield occurs for the first time. The latter quantity cannot be measured easily. In the present paper some neural networks are developed in order to identify the value of Poisson’s ratio. After preparing the input data appropriately, two neural networks are trained, the first one being related to Set 2 of the previous paper. In order to avoid an explicit measurement of the yield depth, the second neural network has to be trained in such a way, that its solution intersects with that of Set 2 at the correct value of Poisson’s ratio. This allows to identify Poisson’s ratio with high accuracy within the domain of finite element data.

Examination of Prestressed Coating/Substrate Systems Using Spherical Indentation—Determination of Film Prestress, Film Modulus, and Substrate Modulus

2019 ◽  
Vol 142 (1) ◽  
Author(s):  
James A. Mills ◽  
Hang Xiao ◽  
Xi Chen
Keyword(s):  
Material Properties ◽  
Indentation Test ◽  
Spherical Indentation ◽  
Indentation Force ◽  
Forward Analysis ◽  
Substrate Properties ◽  
Error Sensitivity Analysis ◽  
Film Substrate

There have been many studies performed with respect to the indentation of thin films affixed to a corresponding substrate base. These studies have primarily focused on determining the mechanical properties of the film. It is the goal of this paper to further understand the role that the film plays and how a potential prestressing of this film has on both the film and substrate base. It is equally important to be able to understand the material properties of the substrate since during manufacturing or long-term use, the substrate properties may change. In this study, we establish through spherical indentation a framework to characterize the material properties of both the substrate and film as well as a method to determine the prestress of the film. It is proposed that through an initial forward analysis, a set of relationships are developed. A single spherical indentation test can then be performed, measuring the indentation force at two prescribed depths, and with the relationships developed from the forward analysis, the material properties of both the film and substrate can be determined. The problem is further enhanced by also developing the capability of determining any equibiaxial stress state that may exist in the film. A generalized error sensitivity analysis of this formulation is also performed systematically. This study will enhance the present knowledge of a typical prestressed film/substrate system as is commonly used in many of today’s engineering and technical applications.

Orthogonal Properties of Human Trabecular Bone by Spherical Indentation Test

2006 ◽  
Vol 326-328 ◽  
pp. 793-796
Author(s):  
Tae Soo Bae ◽  
Tae Soo Lee ◽  
Kui Won Choi
Keyword(s):  
Trabecular Bone ◽  
Apparent Density ◽  
Indentation Test ◽  
Spherical Indentation ◽  
Power Relationship ◽  
Ct Scanner ◽  
Diamond Blade ◽  
Custom Made ◽  
Indentation Tests

The elastic modulus and the apparent density of the trabecular bone were evaluated from spherical indentation tests and Computed Tomography and their relationship was quantified. After the femurs were prepared and embedded with respect to their anatomical orientation, the transverse planes of the trabecular bone specimens were scanned at 1mm intervals using a CT scanner. The metaphyseal regions were sectioned with a diamond-blade saw, producing 8mm cubes. Using a custom-made spherical indentation tester, the cubes were mechanically tested in the anteriorposterior (AP), medial-lateral (ML), and inferior-superior (IS) directions. After determination of modulus from the mechanical testing, the apparent densities of the specimens were measured. The results showed that the IS modulus was significantly greater than both the AP and ML moduli with the AP modulus greater than the ML modulus. This demonstrated that orthogonality was a structural characteristic of the trabecular bone. The power relationship between the modulus and the apparent density was also found to be statistically significant.

Determination of Young's modulus by spherical indentation

1997 ◽  
Vol 12 (9) ◽  
pp. 2459-2469 ◽  
Author(s):  
N. Huber ◽  
D. Munz ◽  
Ch. Tsakmakis
Keyword(s):  
Finite Element ◽  
Young’S Modulus ◽  
Young's Modulus ◽  
Indentation Test ◽  
Spherical Indentation ◽  
Plastic Materials ◽  
Finite Element Calculations ◽  
Loading And Unloading ◽  
Elastic Plastic Materials

In this paper we consider elastic plastic materials that are tested by spherical indentation. Finite element calculations, which take into account nonlinear geometry properties, are carried out in order to determine the influence of the plastic history on the unloading response of the material. Two different iterative methods are proposed for determining Young's modulus under the assumption of a bilinear plasticity law. The first method deals with loading and unloading parts of the indentation test, whereas the second one deals only with unloading parts of the indentation test.

Determination of plastic yield stress from spherical indentation slope curve

2008 ◽  
Vol 62 (15) ◽  
pp. 2260-2262 ◽  
Author(s):  
Wenyi Yan ◽  
Qingping Sun ◽  
Peter D. Hodgson
Keyword(s):  
Yield Stress ◽  
Spherical Indentation ◽  
Plastic Yield

Comparison of the viscoelastic penetration and tensile behaviour of poly(methyl acrylate) and poly(ethyl acrylate)

1979 ◽  
Vol 44 (6) ◽  
pp. 1942-1948 ◽  
Author(s):  
Jaroslav Hrouz ◽  
Michal Ilavský ◽  
Ivan Havlíček ◽  
Karel Dušek
Keyword(s):  
Methyl Acrylate ◽  
Poisson Ratio ◽  
Young Modulus ◽  
Ethyl Acrylate ◽  
Sample Volume ◽  
Viscoelastic Behaviour ◽  
Tensile Behaviour ◽  
Temperature Superposition ◽  
Main Transition

The viscoelastic penetration and tensile behaviour of poly(methyl acrylate) and poly(ethyl acrylate) in the main transition region have been investigated. It was found that the time-temperature superposition could be carried out in the case of the penetration viscoelastic behaviour; the temperature dependence of the penetration and tensile shift factors was the same. The superimposed curves of the penetration and Young modulus allowed us to calculate the dependence of the Poisson ratio and thus to characterize the change in sample volume with deformation. It was demonstrated that the penetration method of determination of the viscoelastic behaviour is equivalent to the tensile method.

scholarly journals Investigation of a Stochastic Inverse Method to Estimate an External Force: Applications to a Wave-Structure Interaction

2012 ◽  
Vol 2012 ◽  
pp. 1-25 ◽  
Author(s):  
S. L. Han ◽  
Takeshi Kinoshita
Keyword(s):  
External Force ◽  
Inverse Method ◽  
Inverse Function ◽  
Wave Structure ◽  
Dynamic Responses ◽  
Structure Interaction ◽  
External Forces ◽  
Interaction Problem ◽  
Wave Structure Interaction

The determination of an external force is a very important task for the purpose of control, monitoring, and analysis of damages on structural system. This paper studies a stochastic inverse method that can be used for determining external forces acting on a nonlinear vibrating system. For the purpose of estimation, a stochastic inverse function is formulated to link an unknown external force to an observable quantity. The external force is then estimated from measurements of dynamic responses through the formulated stochastic inverse model. The applicability of the proposed method was verified with numerical examples and laboratory tests concerning the wave-structure interaction problem. The results showed that the proposed method is reliable to estimate the external force acting on a nonlinear system.

Can indentation technique measure unique elastoplastic properties?

2009 ◽  
Vol 24 (3) ◽  
pp. 784-800 ◽  
Author(s):  
Ling Liu ◽  
Nagahisa Ogasawara ◽  
Norimasa Chiba ◽  
Xi Chen
Keyword(s):  
Critical Strain ◽  
Indentation Test ◽  
Strain Curve ◽  
Spherical Indentation ◽  
Plastic Behavior ◽  
Displacement Curve ◽  
Application Range ◽  
Indentation Technique ◽  
Elastoplastic Properties ◽  
Force Displacement

Indentation is widely used to extract material elastoplastic properties from measured force-displacement curves. Many previous studies argued or implied that such a measurement is unique and the whole material stress-strain curve can be measured. Here we show that first, for a given indenter geometry, the indentation test cannot effectively probe material plastic behavior beyond a critical strain, and thus the solution of the reverse analysis of the indentation force-displacement curve is nonunique beyond such a critical strain. Secondly, even within the critical strain, pairs of mystical materials can exist that have essentially identical indentation responses (with differences below the resolution of published indentation techniques) even when the indenter angle is varied over a large range. Thus, fundamental elastoplastic behaviors, such as the yield stress and work hardening properties (functions), cannot be uniquely determined from the force-displacement curves of indentation analyses (including both plural sharp indentation and deep spherical indentation). Explicit algorithms of deriving the mystical materials are established, and we qualitatively correlate the sharp and spherical indentation analyses through the use of critical strain. The theoretical study in this paper addresses important questions of the application range, limitations, and uniqueness of the indentation test, as well as providing useful guidelines to properly use the indentation technique to measure material constitutive properties.

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