Strain rate sensitivity in nanoindentation creep of hard materials

2007 ◽  
Vol 22 (10) ◽  
pp. 2912-2916 ◽  
Author(s):  
A.A. Elmustafa ◽  
D.S. Stone
Keyword(s):  
Finite Element Analysis ◽  
Strain Rate ◽  
Strain Rate Sensitivity ◽  
Activation Volume ◽  
Rate Sensitivity ◽  
Fused Silica ◽  
Indentation Creep ◽  
Element Analysis ◽  
Hard Materials ◽  
Von Mises

This paper examines the strain rate sensitivity of the hardness νH in relation to the strain rate sensitivity of the flow stress (νσ) in hard solids when there is friction between the indenter and specimen. Finite element analysis is used to simulate indentation creep of von Mises solids with a range of hardness/modulus ratios (H/E*) and coefficients of friction, μ, for indenter–specimen contact. We find that, although the level of H is affected by friction, the ratio νH/νσ as a function of H/E* remains nearly unchanged. Measurements indicate that νH = 0.015 ± 0.02 for fused silica, from which, based on the present analysis, νσ ≈ 0.022 and from which an activation volume of 0.13 nm3 can be estimated for plastic deformation.

Analysis of indentation creep

2010 ◽  
Vol 25 (4) ◽  
pp. 611-621 ◽  
Author(s):  
Don S. Stone ◽  
Joseph E. Jakes ◽  
Jonathan Puthoff ◽  
Abdelmageed A. Elmustafa
Keyword(s):  
Flow Stress ◽  
Strain Rate ◽  
Strain Rate Sensitivity ◽  
Rate Sensitivity ◽  
Fused Silica ◽  
Indentation Creep ◽  
Modulus Ratio ◽  
Element Analysis ◽  
Wide Range ◽  
Self Similar

Finite element analysis is used to simulate cone indentation creep in materials across a wide range of hardness, strain rate sensitivity, and work-hardening exponent. Modeling reveals that the commonly held assumption of the hardness strain rate sensitivity (mH) equaling the flow stress strain rate sensitivity (mσ) is violated except in low hardness/modulus materials. Another commonly held assumption is that for self-similar indenters the indent area increases in proportion to the (depth)2 during creep. This assumption is also violated. Both violations are readily explained by noting that the proportionality “constants” relating (i) hardness to flow stress and (ii) area to (depth)2 are, in reality, functions of hardness/modulus ratio, which changes during creep. Experiments on silicon, fused silica, bulk metallic glass, and poly methyl methacrylate verify the breakdown of the area-(depth)2 relation, consistent with the theory. A method is provided for estimating area from depth during creep.

The strain-rate sensitivity of the hardness in indentation creep

2007 ◽  
Vol 22 (4) ◽  
pp. 926-936 ◽  
Author(s):  
A.A. Elmustafa ◽  
S. Kose ◽  
D.S. Stone
Keyword(s):  
Flow Stress ◽  
Strain Rate ◽  
Strain Rate Sensitivity ◽  
Rate Sensitivity ◽  
Hertzian Contact ◽  
Indentation Creep ◽  
Proportionality Factor ◽  
Element Analysis ◽  
Elastic Deformations ◽  
The Relationship

Finite element analysis is used to simulate indentation creep experiments with a cone-shaped indenter. The purpose of the work is to help identify the relationship between the strain-rate sensitivity of the hardness, νH, and that of the flow stress, νσ in materials for which elastic deformations are significant. In general, νH differs from νσ, but the ratio νH/νσ is found to be a unique function of H/E* where H is the hardness and E* is the modulus relevant to Hertzian contact. νH/νσ approaches 1 for small H/E*, 0 for large H/E*, and is insensitive to work hardening. The trend in νH/νσ as a function of H/E* can be explained based on a generalized analysis of Tabor’s relation in which hardness is proportional to the flow stress H = k × σeff and in which the proportionality factor k is a function of σeff/E*.

Analysis of Indentation Creep

2007 ◽  
Vol 1049 ◽  
Author(s):  
Donald Stone ◽  
A. A. Elmustafa
Keyword(s):  
Flow Stress ◽  
Strain Rate ◽  
Strain Rate Sensitivity ◽  
High Hardness ◽  
Rate Sensitivity ◽  
Constant Load ◽  
Indentation Creep ◽  
Element Analysis ◽  
Wide Range ◽  
Power Law Exponent

AbstractIncreasingly, indentation creep experiments are being used to characterize rate-sensitive deformation in specimens that, due to small size or high hardness, are difficult to characterize by more conventional methods like uniaxial loading. In the present work we use finite element analysis to simulate indentation creep in a collection of materials whose properties vary across a wide range of hardness, strain rate sensitivities, and work hardening exponents. Our studies reveal that the commonly held assumption that the strain rate sensitivity of the hardness equals that of the flow stress is violated except for materials with low hardness/modulus ratios like soft metals. Another commonly held assumption is that the area of the indent increases with the square of depth during constant load creep. This latter assumption is used in an analysis where the experimenter estimates the increase in indent area (decrease in hardness) during creep based on the change in depth. This assumption is also strongly violated. Fortunately, both violations are easily explained by noting that the “constants” of proportionality relating 1) hardness to flow stress and 2) area to (depth)2 are actually functions of the hardness/modulus ratio. Based upon knowledge of these functions it is possible to accurately calculate 1) the strain rate sensitivity of the flow stress from a measurement of the strain rate sensitivity of the hardness and 2) the power law exponent relating area to depth during constant load creep.

Activation volume and strain rate sensitivity in plastic deformation of nanocrystalline Ti

2013 ◽  
Vol 228 ◽  
pp. S254-S256 ◽  
Author(s):  
F. Wang ◽  
B. Li ◽  
T.T. Gao ◽  
P. Huang ◽  
K.W. Xu ◽  
...  
Keyword(s):  
Plastic Deformation ◽  
Strain Rate ◽  
Strain Rate Sensitivity ◽  
Activation Volume ◽  
Rate Sensitivity

Strain rate sensitivity and deformation activation volume of coarse-grained and ultrafine-grained TiNi alloys

2015 ◽  
Vol 102 ◽  
pp. 99-102 ◽  
Author(s):  
D.V. Gunderov ◽  
G. Maksutova ◽  
A. Churakova ◽  
A. Lukyanov ◽  
A. Kreitcberg ◽  
...  
Keyword(s):  
Strain Rate ◽  
Strain Rate Sensitivity ◽  
Activation Volume ◽  
Rate Sensitivity ◽  
Coarse Grained ◽  
Ultrafine Grained

Enhanced Formability in Sheet Metals Produced by Cladding a High Strain-Rate Sensitive Layer

2013 ◽  
Vol 81 (2) ◽  
Author(s):  
X. H. Hu ◽  
P. D. Wu ◽  
D. J. Lloyd ◽  
J. D. Embury
Keyword(s):  
Strain Rate ◽  
Strain Rate Sensitivity ◽  
Volume Fraction ◽  
Rate Sensitivity ◽  
Core Material ◽  
Sensitive Layer ◽  
Element Analysis ◽  
Clad Sheet ◽  
Clad Layer ◽  
The One

The necking behavior of cladding sheets with a rate-sensitive layer cladding on a rate-insensitive core material has been studied. A nonlinear long-wavelength analysis, similar to the one proposed by Hutchinson and Neale (1977, “Influence of Strain-Rate Sensitivity on Necking Under Uniaxial Tension,” Acta Metal., 25, pp. 839–846) for monolithic rate-sensitive materials, is developed to identify the onset of necking in a rate-sensitive clad sheet. This relatively simple analysis is validated by comparing its numerical results with those based on more complicated finite element analysis. It is demonstrated that for monolithic rate-sensitive materials the proposed nonlinear analysis reduces to the one developed by Hutchinson and Neale (1977). For cladding sheets, it is found that the necking strain increases monotonically by increasing the strain-rate sensitivity of the clad layer if the volume fraction of cladding is fixed. It is also revealed that, for fixed strain-rate sensitivity of the clad layer, necking localization is retarded by increasing the volume fraction of the cladding layer.

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