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G M Pharr - One of the best experts on this subject based on the ideXlab platform.
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influences of elasticity on the measurement of power Law Creep parameters by nanoindentation
Journal of The Mechanics and Physics of Solids, 2021Co-Authors: Sudharshan P Phani, W C Oliver, G M PharrAbstract:Abstract Indentation testing is a well-known method to measure the rate dependence of the strength of materials at small scales through a variety of different testing methodologies. In many cases, a power-Law Creep constitutive relationship relating the indentation strain rate to the hardness, or the mean pressure applied to the material by the indenter, is assumed. However, this method of analysis does not explicitly include elastic effects, which for some testing methods may be significant. In this work, a new method of analysis that explicitly considers the elastic effects is presented. The conditions and materials for which the elastic contribution is non-negligible are identified, and simple closed-form analytical expressions are developed to account for the elastic effects. This leads to improvements in the measurement of power Law Creep parameters such as the stress exponent and Creep coefficient. Experimental assessment of the new analysis procedures is presented for amorphous selenium (Se) and calcium fluoride (CaF2). After accounting for the elastic effects, an equivalence of different indentation Creep testing methods is observed for Se due to the fact that this material has a very nearly history independent plastic response and no indentation size effect (ISE). On the other hand, significant differences are observed in the case of CaF2 because of indentation size effects. The findings of this work have important implications for several widely used indentation Creep measurement methods such as the constant strain rate method (CSR) and the strain rate jump test (SRJ). Based on the results, guidelines for performing indentation Creep tests with improved precision and accuracy are presented.
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on the measurement of power Law Creep parameters from instrumented indentation
JOM, 2017Co-Authors: Sudharshan P Phani, W C Oliver, G M PharrAbstract:Recently the measurement of the Creep response of materials at small scales has received renewed interest largely because the equipment required to perform high-temperature nanomechanical testing has become available to an increasing number of researchers. Despite that increased access, there remain several significant experimental and modeling challenges in small-scale mechanical testing at elevated temperatures that are as yet unresolved. In this regard, relating the Creep response observed with high-temperature instrumented indentation experiments to macroscopic uniaxial Creep response is of great practical value. In this review, we present an overview of various methods currently being used to measure Creep with instrumented indentation, with a focus on geometrically self-similar indenters, and their relative merits and demerits from an experimental perspective. A comparison of the various methods to use those instrumented indentation results to predict the uniaxial power Law Creep response of a wide range of materials will be presented to assess their validity.
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measurement of power Law Creep parameters by instrumented indentation methods
Journal of The Mechanics and Physics of Solids, 2013Co-Authors: Erik G Herbert, W C Oliver, G M Pharr, Sangjoon Sohn, James A LamannaAbstract:Abstract New experimental methods are developed to measure the uniaxial power-Law Creep parameters α and n in the relation e = α σ n ( e is the Creep strain rate and σ is the Creep stress) from indentation data obtained with a conical or pyramidal indenter. The methods are based on an analysis of Bower et al., which relates the indentation Creep rate to the uniaxial Creep parameters based on simple assumptions about the constitutive behavior ( Bower et al., 1993 ). Using finite element simulations to establish the influences of finite indenter geometry and transients caused by elasticity, the proposed methods are explored experimentally using amorphous selenium as a model material. This material is well suited for the study because it Creeps at temperatures slightly above ambient in a load-history independent fashion with a stress exponent close to unity. Indentation Creep tests were conducted with a Berkovich indenter using three different loading methods. With a few notable exceptions, the values of both α and n derived from the indentation data are generally in good agreement with those measured in uniaxial compression tests, thus demonstrating the validity of the approach.
Maarten Krabbendam - One of the best experts on this subject based on the ideXlab platform.
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sliding of temperate basal ice on a rough hard bed Creep mechanisms pressure melting and implications for ice streaming
The Cryosphere, 2016Co-Authors: Maarten KrabbendamAbstract:Abstract. Basal ice motion is crucial to ice dynamics of ice sheets. The classic Weertman model for basal sliding over bedrock obstacles proposes that sliding velocity is controlled by pressure melting and/or ductile flow, whichever is the fastest; it further assumes that pressure melting is limited by heat flow through the obstacle and ductile flow is controlled by standard power-Law Creep. These last two assumptions, however, are not applicable if a substantial basal layer of temperate (T ∼ Tmelt) ice is present. In that case, frictional melting can produce excess basal meltwater and efficient water flow, leading to near-thermal equilibrium. High-temperature ice Creep experiments have shown a sharp weakening of a factor 5–10 close to Tmelt, suggesting standard power-Law Creep does not operate due to a switch to melt-assisted Creep with a possible component of grain boundary melting. Pressure melting is controlled by meltwater production, heat advection by flowing meltwater to the next obstacle and heat conduction through ice/rock over half the obstacle height. No heat flow through the obstacle is required. Ice streaming over a rough, hard bed, as possibly in the Northeast Greenland Ice Stream, may be explained by enhanced basal motion in a thick temperate ice layer.
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basal sliding of temperate basal ice on a rough hard bed pressure melting Creep mechanisms and implications for ice streaming
The Cryosphere Discussions, 2016Co-Authors: Maarten KrabbendamAbstract:Basal ice motion is crucial to ice dynamics of ice sheets. The Weertman sliding model for basal sliding over bedrock obstacles proposes that sliding velocity is controlled by pressure melting and/or ductile flow, whichever is the fastest; it further assumes that stoss-side melting is limited by heat flow through the obstacle and ductile flow is controlled by Power Law Creep. These last two assumptions, it is argued here, are invalid if a substantial basal layer of temperate (T ~ Tmelt) ice is present. In that case, frictional melting results in excess basal meltwater and efficient water flow, leading to near-thermal equilibrium. Stoss-side melting is controlled by melt water production, heat advection by flowing meltwater to the next obstacle, and heat conduction through ice/rock over half the obstacle height. No heat flow through the obstacle is required. High temperature ice Creep experiments have shown a sharp weakening of a factor 5–10 close to Tmelt, implying breakdown of Power Law Creep and probably caused by a deformation-mechanism switch to grain boundary pressure melting. Ice streaming over a rough, hard bed, as likely in the Northeast Greenland Ice Stream, may be explained by enhanced basal motion in a thick temperate ice layer.
Yangtse Cheng - One of the best experts on this subject based on the ideXlab platform.
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indentation of power Law Creep solids by self similar indenters
Materials Science and Engineering A-structural Materials Properties Microstructure and Processing, 2010Co-Authors: Weimin Chen, Yangtse ChengAbstract:For Creep solids obeying the power Law under tension proposed by Tabor, namely sigma = b(epsilon) over dot(m), it has been established through dimensional analysis that for self-similar indenters the load F versus indentation depth h can be expressed as F(t) = bh(2)(t)[(h) over dot(t)/h(t)](m)Pi(alpha) where the dimensionless factor Pi(alpha) depends on material parameters such as m and the indenter geometry. In this article, we show that by generalizing the Tabor power Law to the general three dimensional case on the basis of isotropy, this factor can be calculated so that indentation test can be used to determine the material parameters b and m appearing in the original power Law. Hence indentation test can replace tension test. This could be a distinct advantage for materials that come in the form of thin films, coatings or otherwise available only in small amounts. To facilitate application values of this constant are given in tabulated form for a range of material parameters. (C) 2010 Elsevier B.V. All rights reserved.
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scaling relationships in indentation of power Law Creep solids using self similar indenters
Philosophical Magazine Letters, 2001Co-Authors: Yangtse Cheng, Chemin ChengAbstract:We use dimensional analysis to derive scaling relationships for self-similar indenters indenting solids that exhibit power-Law Creep. We identify the parameter that represents the indentation strain rate. The scaling relationships are applied to several types of indentation Creep experiment with constant displacement rate, constant loading rate or constant ratio of loading rate over load. The predictions compare favourably with experimental observations reported in the literature. Finally, a connection is found between Creep and 'indentation-size effect' (i.e. changing hardness with indentation depth or load).
W C Oliver - One of the best experts on this subject based on the ideXlab platform.
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influences of elasticity on the measurement of power Law Creep parameters by nanoindentation
Journal of The Mechanics and Physics of Solids, 2021Co-Authors: Sudharshan P Phani, W C Oliver, G M PharrAbstract:Abstract Indentation testing is a well-known method to measure the rate dependence of the strength of materials at small scales through a variety of different testing methodologies. In many cases, a power-Law Creep constitutive relationship relating the indentation strain rate to the hardness, or the mean pressure applied to the material by the indenter, is assumed. However, this method of analysis does not explicitly include elastic effects, which for some testing methods may be significant. In this work, a new method of analysis that explicitly considers the elastic effects is presented. The conditions and materials for which the elastic contribution is non-negligible are identified, and simple closed-form analytical expressions are developed to account for the elastic effects. This leads to improvements in the measurement of power Law Creep parameters such as the stress exponent and Creep coefficient. Experimental assessment of the new analysis procedures is presented for amorphous selenium (Se) and calcium fluoride (CaF2). After accounting for the elastic effects, an equivalence of different indentation Creep testing methods is observed for Se due to the fact that this material has a very nearly history independent plastic response and no indentation size effect (ISE). On the other hand, significant differences are observed in the case of CaF2 because of indentation size effects. The findings of this work have important implications for several widely used indentation Creep measurement methods such as the constant strain rate method (CSR) and the strain rate jump test (SRJ). Based on the results, guidelines for performing indentation Creep tests with improved precision and accuracy are presented.
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on the measurement of power Law Creep parameters from instrumented indentation
JOM, 2017Co-Authors: Sudharshan P Phani, W C Oliver, G M PharrAbstract:Recently the measurement of the Creep response of materials at small scales has received renewed interest largely because the equipment required to perform high-temperature nanomechanical testing has become available to an increasing number of researchers. Despite that increased access, there remain several significant experimental and modeling challenges in small-scale mechanical testing at elevated temperatures that are as yet unresolved. In this regard, relating the Creep response observed with high-temperature instrumented indentation experiments to macroscopic uniaxial Creep response is of great practical value. In this review, we present an overview of various methods currently being used to measure Creep with instrumented indentation, with a focus on geometrically self-similar indenters, and their relative merits and demerits from an experimental perspective. A comparison of the various methods to use those instrumented indentation results to predict the uniaxial power Law Creep response of a wide range of materials will be presented to assess their validity.
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measurement of power Law Creep parameters by instrumented indentation methods
Journal of The Mechanics and Physics of Solids, 2013Co-Authors: Erik G Herbert, W C Oliver, G M Pharr, Sangjoon Sohn, James A LamannaAbstract:Abstract New experimental methods are developed to measure the uniaxial power-Law Creep parameters α and n in the relation e = α σ n ( e is the Creep strain rate and σ is the Creep stress) from indentation data obtained with a conical or pyramidal indenter. The methods are based on an analysis of Bower et al., which relates the indentation Creep rate to the uniaxial Creep parameters based on simple assumptions about the constitutive behavior ( Bower et al., 1993 ). Using finite element simulations to establish the influences of finite indenter geometry and transients caused by elasticity, the proposed methods are explored experimentally using amorphous selenium as a model material. This material is well suited for the study because it Creeps at temperatures slightly above ambient in a load-history independent fashion with a stress exponent close to unity. Indentation Creep tests were conducted with a Berkovich indenter using three different loading methods. With a few notable exceptions, the values of both α and n derived from the indentation data are generally in good agreement with those measured in uniaxial compression tests, thus demonstrating the validity of the approach.
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Indentation power-Law Creep of high-purity indium
Metallurgical and Materials Transactions A, 2007Co-Authors: B N Lucas, W C OliverAbstract:Using a variety of depth-sensing indentation techniques, the Creep response of high-purity indium, from room temperature to 75 degrees C, was measured. The dependence of the hardness on the variables of indentation strain rate (stress exponent for Creep (n)) and temperature (apparent activation energy for Creep (Q)) and the existence of a steady-state behavior in an indentation test with a Berkovich indenter were investigated. It was shown for the first time that the indentation strain rate ((h) over dot/h) could be held constant during an experiment using a Berkovich indenter, by maintaining the loading rate divided by the load ((P) over dot/P) constant. The apparent activation energy for indentation Creep was found to be 78 kJ/mol, in accord with the activation energy for self-diffusion in the material. Finally, by performing (P) over dot/P change experiments, it was shown that a steady-state path independent of hardness could be reached in an indentation test with a geometrically similar indenter.
Robert M Mcmeeking - One of the best experts on this subject based on the ideXlab platform.
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power Law Creep with interface slip and diffusion in a composite material
Mechanics of Materials, 1995Co-Authors: Robert M McmeekingAbstract:Abstract The leading order solution for the power Law Creep of a matrix around a rigid finite fiber is developed. The matrix is well bonded to the fiber but the interface is assumed to be capable of slip with a drag which is linearly proportional to the slip velocity. In addition, mass transport by stress driven diffusion is assumed also to be possible at the interface between the fiber and the matrix. It is found that when there is no slip or interface mass transport, the composite has a high Creep strength compared to the matrix. However, both slip and mass transport acting individually or together are capable of reducing the Creep strength of the composite material. If slip occurs very readily or mass transport is very rapid or both, the Creep strength of the composite can fall below that of the pure matrix material. It is notable that mass transport and interface slip with a linear rheology have an identical effect on the Creep strength of the composite material.
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power Law Creep of a composite material containing discontinuous rigid aligned fibers
International Journal of Solids and Structures, 1993Co-Authors: Robert M McmeekingAbstract:Abstract An asymptotic analysis is presented for the power Law Creep of a matrix containing discontinuous rigid aligned fibers. The fibers analysed have a high aspect ratio. As a result, the fiber length is much greater than both the fiber diameter and the spacing between neighboring fibers. For this situation, flow around the fiber ends can be neglected when the Creep strength is being calculated. When the matrix is not slipping on the fiber surface or is nearly stuck, shearing flow dominates the behavior. The radial gradient of shear stress is balanced by the axial gradient of hydrostatic stress. Longitudinal, radial and circumferential deviatoric stresses are negligible. The resulting power Law Creep rate of the composite material is inversely proportional to the fiber aspect ratio raised to the power 1 + 1/n where n is the Creep index. The fiber volume fraction also influences the Creep rate. When the matrix slips freely on the fiber surface, or nearly so, stretching dominates the matrix flow. In this situation, the composite Creep strength is not much better than the unreinforced matrix.
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power Law Creep of powder bonded by isolated contacts
International Journal of Mechanical Sciences, 1992Co-Authors: Liisa T Kuhn, Robert M McmeekingAbstract:Abstract The deformation of powder due to power-Law Creep near the interparticle contacts is modeled. It is assumed that the plastic dissipation is dominated by the rate of approach of neighboring particles and that the effect of tangential motion can be neglected. To characterize the Creep Law, the macroscopic strain rate in the powder aggregate is specified and the energy dissipated in power-Law Creep is computed. This work rate is used in a potential to determine the macroscopic Creep parameters. The effective macroscopic shear and dilatational Creep properties resulting from this model depend on the relative density of the powder. The Creep rates are infinite at random close-packed density. A feature of the Creep Law is a high sensitivity to changes in deviatoric stress when the stress state is nearly hydrostatic and the Creep exponent is high.
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Creep of power Law material containing spherical voids
Journal of Applied Mechanics, 1992Co-Authors: Petros Athanasios Sofronis, Robert M McmeekingAbstract:Finite element calculations have been carried out for spherical unit cells containing a concentric spherical hole to characterize the power Law Creep of a material containing voids. Axisymmetric states of macroscopic stress were applied to the unit cells ranging from purely hydrostatic loading to purely deviatoric stressing. The results of the unit cell calculations are approximated well by a Creep potential for the macroscopic behavior of a porous material. This potential agrees with the unit cell results for purely hydrostatic stress and purely deviatoric stress and involves a simple elliptical interpolation in between. The model predicts quite well the ratio of transverse to axial strain rate in uniaxial compression tests.