Strain rate sensitivity of hardness in indentation creep with conical and spherical indenters taking into consideration elastic deformations

2021 ◽  
Vol 212 ◽  
pp. 143-151
Author(s):  
Yousuf S. Mohammed ◽  
D.S. Stone ◽  
A.A. Elmustafa
Keyword(s):  
Strain Rate ◽  
Strain Rate Sensitivity ◽  
Rate Sensitivity ◽  
Indentation Creep ◽  
Elastic Deformations

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*.

scholarly journals Depth-Sensing Indentation Creep Behavior of Nanostructured Thermal Barrier Coatings from As-Synthesized t’-8YSZ Feedstocks

Nanomaterials ◽  
2019 ◽  
Vol 10 (1) ◽  
pp. 38
Author(s):  
Feifei Zhou ◽  
Min Liu ◽  
Yaming Wang ◽  
You Wang ◽  
Chunming Deng
Keyword(s):  
Strain Rate ◽  
Thermal Barrier Coatings ◽  
Strain Rate Sensitivity ◽  
Creep Behavior ◽  
Rate Sensitivity ◽  
Indentation Creep ◽  
Thermal Barrier ◽  
Depth Sensing ◽  
Barrier Coatings ◽  
Nano Indentation

Nano-indentation is a popular method to characterize the micromechanical properties of nanostructured 8YSZ coatings. However, little research has focused on the creep behavior of nano-indentation and only the elastic modulus and nanohardness have been analyzed. Herein, for the first time, the nano-indentation creep behavior of plasma-sprayed nanostructured 8YSZ coatings using as-prepared nanostructured non-transformable tetragonal (t’) feedstocks was investigated. The indentation creep behavior can be well characterized by the power-law equation and the strain rate sensitivity has been calculated in light of the equation. The strain rate sensitivity was sensitive to the load and the reasons were analyzed in detail. The current results can further guide and design thermal barrier coatings from the point of indentation creep property.

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.

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.

scholarly journals Twinning-Induced Abnormal Strain Rate Sensitivity and Indentation Creep Behavior in Nanocrystalline Mg Alloy

Materials ◽  
2021 ◽  
Vol 14 (22) ◽  
pp. 7104
Author(s):  
Shilun Yu ◽  
Yingchun Wan ◽  
Chuming Liu ◽  
Zhiyong Chen ◽  
Xiangyang Zhou
Keyword(s):  
Strain Rate ◽  
Strain Rate Sensitivity ◽  
Creep Behavior ◽  
Nanocrystalline Materials ◽  
Volume Fraction ◽  
Chemical Properties ◽  
Rate Sensitivity ◽  
Coarse Grained ◽  
Indentation Creep ◽  
Zr Alloy

Nanocrystalline materials exhibit many unique physical and chemical properties with respect to their coarse-grained counterparts due to the high volume fraction of grain boundaries. Research interests on nanocrystalline materials around the world have been lasting over the past decades. In this study, we explored the room temperature strain rate sensitivity and creep behavior of the nanocrystalline Mg–Gd–Y–Zr alloy by using a nanoindentation technique. Results showed that the hardness and creep displacements of the nanocrystalline Mg–Gd–Y–Zr alloy decreased with increasing loading strain rate. That is, the nanocrystalline Mg–Gd–Y–Zr alloy showed negative strain rate sensitivity and its creep behavior also exhibited negative rate dependence. It was revealed that the enhanced twinning activities at higher loading strain rates resulted in reduced hardness and creep displacements. The dominant creep mechanism of the nanocrystalline Mg–Gd–Y–Zr alloy is discussed based on a work-of-indentation theory in this paper.

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.

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