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

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.

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.

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 Strain Rate Sensitivity of Alloys 800H and 617

2013 ◽  
Author(s):  
J. K. Wright ◽  
J. A. Simpson ◽  
R. N. Wright ◽  
L. J. Carroll ◽  
T. L. Sham
Keyword(s):  
High Temperature ◽  
Flow Stress ◽  
Strain Rate ◽  
Strain Rate Sensitivity ◽  
Rate Sensitivity ◽  
Temperature Limit ◽  
Applied Strain ◽  
Alloy 800H ◽  
Alloy 617 ◽  
Temperature Heat

The flow stress of many materials is a function of the applied strain rate at elevated temperature. The magnitude of this effect is captured by the strain rate sensitivity parameter “m”. The strain rate sensitivity of two face–center cubic solid solution alloys that are proposed for use in high temperature heat exchanger or steam generator applications, Alloys 800H and 617, has been determined as a function of temperature over that range of temperatures relevant for these applications. In addition to determining the strain rate sensitivity, it is important for nuclear design within Section III of the ASME Boiler and Pressure Vessel Code to determine temperature below which the flow stress is not affected by the strain rate. This temperature has been determined for both Alloy 800H and Alloy 617. At high temperature the strain rate sensitivity of the two alloys is significant and they have similar m values. For Alloy 617 the temperature limit below which little or no strain rate sensitivity is observed is approximately 700°C. For Alloy 800H this temperature is approximately 650°C.

Strain Rate Dependence of the Flow Stress and Work-Hardening of Single Crystals of NI3(Al,Hf)B

1994 ◽  
Vol 364 ◽  
Author(s):  
S. S. Ezz ◽  
Y. Q. Sun ◽  
P. B. Hirsch
Keyword(s):  
Flow Stress ◽  
Strain Rate ◽  
Temperature Dependence ◽  
Single Crystals ◽  
Yield Stress ◽  
Strain Rate Sensitivity ◽  
Work Hardening ◽  
Room Temperature ◽  
Rate Sensitivity ◽  
Controlling Mechanism

AbstractThe strain rate sensitivity ß of the flow stress τ is associated with workhardening and β=(δτ/δln ε) is proportional to the workhardening increment τh = τ - τy, where τy is the strain rate independent yield stress. The temperature dependence of β/τh reflects changes in the rate controlling mechanism. At intermediate and high temperatures, the hardening correlates with the density of [101] dislocations on (010). The nature of the local obstacles at room temperature is not established.

Microstructure and Plasticity of Hot Deformed 5083 Aluminum Alloy Produced by Rapid Solidification and Hot Extrusion / Badania Mikrostruktury I Plastyczności Odkształcanego Na Gorąco Szybko-Krystalizowanego I Wyciskanego Stopu Aluminium 5083

2012 ◽  
Vol 57 (4) ◽  
pp. 1253-1259 ◽  
Author(s):  
T. Tokarski ◽  
Ł. Wzorek ◽  
H. Dybiec
Keyword(s):  
Aluminum Alloy ◽  
High Temperature ◽  
Flow Stress ◽  
Strain Rate ◽  
Strain Rate Sensitivity ◽  
Rate Sensitivity ◽  
Temperature Range ◽  
Rapidly Solidified ◽  
5083 Aluminum Alloy ◽  
Conventionally Cast

The objective of the present study is to analyze the mechanical properties and thermal stability for rapidly solidified and extruded 5083 aluminum alloy (RS). Compression tests were performed in order to estimate flow stress and strain rate sensitivity relation for 5083 alloy in the temperature range of 20°C to 450°C. For the comparison purposes, conventionally cast and extruded industrial material (IM) was studied as well. Deformation tests performed at room temperature conditions show that rapidly solidified material exhibits about 40% higher yield stress (YS=320 MPa) than conventionally cast material (YS=180 MPa), while the deformation at 450°C results in significant decrease of flow stress parameters for RS material (YS=20 MPa) in comparison to IM material (YS=40 MPa). Strain rate sensitivity parameter determined for high temperature conditions indicates superplasticity behavior of RS material. Structural observations show that under conditions of high-temperature deformation there are no operating recrystallization mechanisms. In general, grain size below 1µm and size of reinforcing phases below 50 nm is preserved within the used deformation temperature range.

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