Topic
Indentation
About: Indentation is a research topic. Over the lifetime, 13002 publications have been published within this topic receiving 340476 citations.
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TL;DR: In this article, the shape of the deformed shells depends on the deformation rate, the reduced volume V/V0 and the Foppl-von Karman number γ.
Abstract: The deformation of thin spherical shells by applying an external pressure or by reducing the volume is studied by computer simulations and scaling arguments. The shape of the deformed shells depends on the deformation rate, the reduced volume V/V0 and the Foppl–von Karman number γ. For slow deformations the shell attains its ground state, a shell with a single indentation, whereas for large deformation rates the shell appears crumpled with many indentations. The rim of the single indentation undergoes a shape transition from smooth to polygonal for γ7000(ΔV/V0)− 3/4. For the smooth rim the elastic energy scales like γ1/4 whereas for the polygonal indentation we find a much smaller exponent, even smaller than the exponent 1/6 that is predicted for stretching ridges. The relaxation of a shell with multiple indentations towards the ground state follows an Ostwald ripening type of pathway and depends on the compression rate and on the Foppl–von Karman number. The number of indentations decreases as a power law with time t following Nind~t− 0.375 for γ=8×103 and γ=8×104 whereas for γ=8×105 the relaxation time is longer than the simulation time.
84 citations
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TL;DR: In this article, a two-parameter "area function" characterizing the depth-dependent projected area of an indenter was introduced and applied to a Berkovich tip, corresponding to the effective tip radius and effective cone angle.
Abstract: A two-parameter “area function” characterizing the depth-dependent projected area of an indenter was introduced and applied to a Berkovich tip. The two parameters have physical meaning, corresponding to the effective tip radius and effective cone angle. The indenter tip was calibrated on a commercial load-controlled Nano Indentert® XP (MTS Systems Corp., Eden Prairie, MN). All calibrations were carried out using the procedure of Oliver and Pharr [J. Mater. Res. 7, 1564 (1992)] using several homogeneous materials. Plane-strain modulus and hardness values deconvoluted from indentation load–displacement traces using the calibrated two-parameter area function compared well with the values determined using the empirical eight-parameter area function of Oliver and Pharr.
84 citations
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TL;DR: In this article, the authors describe a dynamic indentation (DI) technique suitable for the determination of the high strain rate flow behavior of ductile metals and alloys and illustrate its use by characterizing the high-strain rate flow behaviour of iron and OFHC copper.
Abstract: The objective of the paper is to describe a dynamic indentation (DI) technique suitable for the determination of the high strain rate flow behaviour of ductile metals and alloys and illustrate its use by characterizing the high strain rate flow behaviour of iron and OFHC copper. The DI technique is first described in detail and the dynamic hardness-strain data of iron and copper obtained using the technique is presented. It is also demonstrated that it is a suitable technique for characterizing the high strain rate flow behaviour as long as certain validity conditions are met. It is shown that these validity conditions are fully met in the case of copper and at low strain levels in iron. The reliability of the DI technique is finally demonstrated by comparing the present data with the literature data on similar materials and finally a critique of the DI technique is provided.
84 citations
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TL;DR: In this article, a review of current analytical equations to model the nanoindentation process is made and compared to finite element analysis (FEA) for a rigid, spherically shaped indenter acting on an elastic two-phase system of an elastic layer that is more compliant than the underlying elastic substrate.
Abstract: Finite element analysis (FEA) is used to model the nanoindentation process for a rigid, spherically shaped indenter acting on an elastic two-phase system of an elastic layer that is more compliant than the underlying elastic substrate. A review of current analytical equations to model this process is made and compared to FEA. The FEA results may be expressed analytically by a simple function that describes the reduced modulus value obtained with Oliver and Pharr's method for any modulus value, thickness of layer or radius of the indenter tip. This function is used to investigate B?ckle's rule, that to measure the properties of a layer, the indentation depth should be 10% or less of the total layer thickness. The results show that B?ckle's rule is invalid for layer thicknesses below 5??m and a new rule is developed which depends on the layer thickness, the indenter radius and the ratio of the reduced moduli of the substrate and overlayer. This rule is based on FEA data. We present a guide to the analysis of the maximum depth that may be indented in order to keep the uncertainty in the reduced modulus for the layer to better than 10%.
84 citations
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TL;DR: In this article, a method to measure the complex compliance (or modulus) of linearly viscoelastic materials is presented using nanoindentation with a spherical indenter.
Abstract: A method to measure the complex compliance (or modulus) of linearly viscoelastic materials is presented using nanoindentation with a spherical indenter The Hertzian solution for an elastic indentation problem, in combination with a hereditary integral operator proposed by Lee and Radok (Journal of Applied Mechanics 27, 1960, 438–444) for the situation of non-decreasing indentation contact area, was used to derive formulas for the complex viscoelastic functions in the frequency-domain The formulas are most suitable for frequencies lower than a frequency limit such that the condition of non-decreasing contact area holds; they are reasonably good approximation at higher frequencies under which decreasing contact area occurs and the Ting (Journal of Applied Mechanics 33, 1966, 845–854) approach for arbitrary contact area history is needed Nanoindentation tests were conducted on both polycarbonate and polymethyl methacrylate under a harmonic indentation load superimposed on either step or ramp indentation load, while the resulting displacement under steady state was recorded The load and displacement data at each frequency were processed using the derived formulas to determine the viscoelastic functions in the frequency-domain The same materials were also tested using a dynamic mechanical analysis (DMA) apparatus to determine the complex viscoelastic functions The DMA and nanoindentation results were compared and found in a good agreement, indicating the validity of the new method presented
84 citations