The Indentation Elastic Response - Indentation Shape and the Stress Distribution

MRS Proceedings ◽

10.1557/proc-356-699 ◽

1994 ◽

Vol 356 ◽

Author(s):

B. C. Hendrix ◽

Ke-Wei Xu ◽

Jun-Hai Liu ◽

Jia-Wen He

Keyword(s):

Elastic Recovery ◽

Transversely Isotropic ◽

Elastic Response ◽

Consistent Model ◽

Self Consistent ◽

Unique Model ◽

Transversely Isotropic Materials ◽

Fundamental Value ◽

Further Development

AbstractThe unloading of an indentation provides information about the shape of the indentation and the elastic properties of the materials. The assumptions of axisymmetry and material isotropy are critically examined, and a model for transversely isotropic materials is compared to measurements on single crystals. The methods used to infer the area of the indentation from the unloading curve are examined. The area is a fundamental value for the determination of hardness, modulus, and other mechanical properties in the so-called nano-indentor and other continuously monitored indentor techniques. The models of elastic recovery which are currently used are found to lack the flexibility to model the parameters which determine indentation depth. If the current self-consistent model is extended to cover the important aspects of the unloading, the area of the indentation is still not determined uniquely. Guidelines for further development of a unique model are suggested.

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Determination of elastic constants of transversely isotropic materials by combining vibration testing and numerical method

Polymer Composites ◽

10.1002/pc.10535 ◽

2001 ◽

Vol 22 (2) ◽

pp. 242-249 ◽

Cited By ~ 1

Author(s):

Shun-Fa Hwang ◽

Chao-Shui Chang ◽

Kung-Lin Chang

Keyword(s):

Numerical Method ◽

Elastic Constants ◽

Transversely Isotropic ◽

Vibration Testing ◽

Isotropic Materials ◽

Transversely Isotropic Materials

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Comparison of finite-element and homogenization methods for modelling the viscoplastic behaviour of a S2–columnar-ice polycrystal

Annals of Glaciology ◽

10.3189/172756400781820598 ◽

2000 ◽

Vol 30 ◽

pp. 115-120 ◽

Cited By ~ 10

Author(s):

Jacques Meyssonnier ◽

Armelle Philip

Keyword(s):

Finite Element ◽

Strain Rate ◽

Transversely Isotropic ◽

Uniform Strain ◽

Upper And Lower Bounds ◽

Uniform Stress ◽

Consistent Model ◽

Self Consistent ◽

Polycrystalline Ice ◽

Homogenization Methods

AbstractThe main homogenization schemes used to model the behaviour of polycrystalline ice are assessed by studying the particular case of a two-dimensional polycrystal which represents natural S2–columnar ice. The results of the uniform-stress, uniform-strain-rate and one-site self-consistent models are compared to finite-element computations. The comparisons were made using the same model of grain, described as a continuous transversely isotropic medium, in the linear and non-linear cases. The uniform-stress and uniform-strain-rate models provide upper and lower bounds for the macroscopic fluidity which are too far from each other to be useful when a degree of anisotropy relevant to ice is considered. Although the self-consistent model gives a weak representation of the interaction between a grain and its surroundings, due to the strong anisotropy of the ice crystal, the resulting macroscopic behaviour is found to be acceptable when compared to the results from finite-element computations.

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Self-Consistent Determination of Time-Dependent Behavior of Metals

Journal of Applied Mechanics ◽

10.1115/1.3157590 ◽

1981 ◽

Vol 48 (1) ◽

pp. 41-46 ◽

Cited By ~ 55

Author(s):

G. J. Weng

Keyword(s):

Driving Forces ◽

Pure Shear ◽

Time Dependent ◽

Hardening Law ◽

Dependent Behavior ◽

Consistent Model ◽

Self Consistent ◽

The Matrix ◽

Latent Hardening

Though Kro¨ner’s self-consistent model is not fully consistent in the elastic-plastic deformation of polycrystals, it is found to be perfectly consistent in the time-dependent deformation of such materials. Hill’s model, on the other hand, should be used with a modified constraint tensor containing the elastic moduli of the matrix in that case. Kro¨ner’s model is supplemented with a physically consistent constitutive equation for the slip system; these, together with Weng’s inverse method, form the basis of a self-consistent determination of time-dependent behavior of metals. The kinematic component of the latent hardening law and the residual stress introduced in more favorably oriented grains are the two major driving forces for recovery and the Bauschinger effect in creep. The proposed method was applied to predict the creep and recovery strains of a 2618-T61 Aluminum alloy under pure shear, step and nonradial loading. The predicted results are seen to be in generally good agreement with the test data.

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Determination of single crystal elastic constants in textured polycrystalline materials: inverse approach coupling x-ray diffraction and self consistent model applied to a copper sample

Matériaux & Techniques ◽

10.1051/mattech:2004014 ◽

2004 ◽

Vol 92 (3-4) ◽

pp. 29-34

Author(s):

N. Guibert ◽

L. Gosmain ◽

Ch. Valot ◽

C. Valot ◽

K. Inal ◽

...

Keyword(s):

Single Crystal ◽

Elastic Constants ◽

Copper Sample ◽

Polycrystalline Materials ◽

X Ray Diffraction ◽

X Ray ◽

Inverse Approach ◽

Consistent Model ◽

Self Consistent

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Incompatibility Stresses and Elastic Energy Stored in Polycrystalline Materials

Materials Science Forum ◽

10.4028/www.scientific.net/msf.638-642.3827 ◽

2010 ◽

Vol 638-642 ◽

pp. 3827-3832 ◽

Cited By ~ 4

Author(s):

Andrzej Baczmanski ◽

Roman Wawszczak ◽

Wilfrid Seiler ◽

Chedly Braham ◽

S. Wroński ◽

...

Keyword(s):

Stress Field ◽

Elastic Energy ◽

Ferritic Steel ◽

Diffraction Method ◽

Polycrystalline Materials ◽

Consistent Model ◽

Self Consistent ◽

Euler Space ◽

Cold Rolled

ray diffraction method is used to determine the stress field in polycrystalline materials. The measurement of peak shifts enables the determination of the macrostresses and the plastic incompatibility stresses (intergranular stresses). In the interpretation of the experimental results self-consistent model of elatoplastic deformation is used. In the present work, the plastic incompatibility stresses and the elastic energy stored in cold rolled brass and ferritic steel were determinate. The results are discussed and presented in Euler space.

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Quantitative Prediction of Cold Rolling Textures in Low-Carbon Steel by Means of the Lamel Model

Textures and Microstructures ◽

10.1155/tsm.31.109 ◽

1999 ◽

Vol 31 (3) ◽

pp. 109-149 ◽

Cited By ~ 109

Author(s):

P. Van Houtte ◽

L. Delannay ◽

I. Samajdar

Keyword(s):

Carbon Steel ◽

Cold Rolling ◽

Low Carbon Steel ◽

Quantitative Prediction ◽

Low Carbon ◽

New Model ◽

Taylor Models ◽

Consistent Model ◽

Self Consistent ◽

Further Development

Rolling textures of low-carbon steel predicted by full constraints and relaxed constraints Taylor models, as well by a self-consistent model, are quantitatively compared to experimental results. It appears that none of these models really performs well, the best results being obtained by the Pancake model. Anew model (“Lamel model”) is then proposed as a further development of the Pancake model. It treats a stack of two lamella-shaped grains at a time. The new model is described in detail, after which the results obtained for rolling of low-carbon steel are discussed. The prediction of the overall texture now is quantitatively correct. However, the γ-fibre components are better predicted than the α-fibre ones. Finally it is concluded that further work is necessary, as the same kind of success is not guaranteed for other cases, such as rolling of f.c.c, materials.

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