This document discusses using nanoindentation to measure the time-dependent constitutive behavior of viscoelastic solids over a wide range of time and frequency. It aims to extend nanoindentation techniques to analyze materials' frequency-domain responses over short times and time-domain responses over long times using a simple flat punch indentation method. The document also models the instrumentation involved in nanoindentation, accounting for the indenter's time-dependent properties, in order to accurately measure the time-dependent properties of the test materials.
M. Dimitrijevic/ V. Radovanovic: D-deformed Wess-Zumino Model and its Renorma...SEENET-MTP
The document summarizes a presentation on D-deformed Wess-Zumino model and its renormalizability properties. It discusses deforming spaces and symmetries using twist formalism. Specifically, it describes how an Abelian twist can deform Poincaré symmetry to obtain noncommutative spacetime while preserving associativity. This allows for construction of D-deformed supersymmetric theories like the Wess-Zumino model, along with investigating their renormalizability.
This document summarizes research on quantitatively evaluating neuroplastic biomaterials for rehabilitation in stroke patients. It measured resistive torque and electromyograms from eight lower limb muscles in patients. The resistive torque showed hysteresis curves that were velocity-dependent, a characteristic of stroke. Electromyograms showed both short latency reflexes via the spinal cord and long latency reflexes via the cerebral cortex. Modeling showed intrinsic viscoelasticity could be modeled with a differential equation, while reflex components could be modeled with a double exponential function. Future work aims to improve these models and apply information technology and numerical modeling in healthcare education.
This document presents a simple phenomenological approach to modeling nanoindentation creep using conventional spring and dashpot elements. It describes how creep, which is the time-dependent increase in depth under a held load, can be modeled for a variety of materials using Maxwell and Voigt models. Equations are presented that relate the depth increase over time to the elastic modulus and viscosity of the material being tested. A method is described for fitting experimental nanoindentation data, including holding periods, to these equations to determine material properties while accounting for creep. The approach aims to provide an accessible way to analyze creep in nanoindentation that can be incorporated into computer programs.
Process of Nanoindentation and use of finite element modellingD.R. Kartikayan
This document provides an overview of nanoindentation testing for measuring material properties. It discusses why nanoindentation is used, the requirements and procedure for nanoindentation testing, and how to analyze the load-displacement curves obtained from testing. Factors that can affect nanoindentation results are also covered, as well as how finite element modeling can be used to better interpret nanoindentation data and account for these influencing factors.
La nanoindentación es una prueba de dureza que mide las propiedades mecánicas de un material a escala nanométrica mediante el uso de una pequeña punta que indenta la muestra. La carga y desplazamiento se miden continuamente para determinar la dureza y el módulo de Young. Ofrece ventajas como ser rápido, permitir múltiples medidas en una misma muestra, y analizar muestras pequeñas como películas delgadas. Sin embargo, el equipo es muy sensible a vibraciones y cambios térmicos
Nanoindentation is a technique used to determine material properties such as hardness and elastic modulus at small length scales. It works by pressing an indenter with a very small tip into the material and measuring the resulting load and displacement. Factors like thermal drift, machine compliance, and real tip geometry must be accounted for when analyzing the load-displacement data to determine properties. Commercial nanoindentation machines use various methods like capacitive sensing or optical lever systems to precisely measure displacement during indentation testing.
1. Nanoindentation was used to characterize the mechanical properties of various nanostructures such as carbon nanotubes, silver nanowires, and zinc oxide nanobelts.
2. Pressure-induced phase transformations were observed in materials like silicon and germanium during nanoindentation. Pop-in and pop-out events indicated phase changes.
3. Nanoindentation helped determine the mechanical properties of thin films, MEMS structures, and the effects of residual stress. It was also used to study superlattices.
El documento describe diferentes métodos para medir la dureza de los materiales, incluyendo ensayos de rayado, penetración y dinámicos. Explica métodos como Brinell, Vickers, Rockwell, Shore y Knoop, detallando el procedimiento y características de cada uno. El documento provee información sobre cómo medir y comparar la dureza de diferentes materiales.
M. Dimitrijevic/ V. Radovanovic: D-deformed Wess-Zumino Model and its Renorma...SEENET-MTP
The document summarizes a presentation on D-deformed Wess-Zumino model and its renormalizability properties. It discusses deforming spaces and symmetries using twist formalism. Specifically, it describes how an Abelian twist can deform Poincaré symmetry to obtain noncommutative spacetime while preserving associativity. This allows for construction of D-deformed supersymmetric theories like the Wess-Zumino model, along with investigating their renormalizability.
This document summarizes research on quantitatively evaluating neuroplastic biomaterials for rehabilitation in stroke patients. It measured resistive torque and electromyograms from eight lower limb muscles in patients. The resistive torque showed hysteresis curves that were velocity-dependent, a characteristic of stroke. Electromyograms showed both short latency reflexes via the spinal cord and long latency reflexes via the cerebral cortex. Modeling showed intrinsic viscoelasticity could be modeled with a differential equation, while reflex components could be modeled with a double exponential function. Future work aims to improve these models and apply information technology and numerical modeling in healthcare education.
This document presents a simple phenomenological approach to modeling nanoindentation creep using conventional spring and dashpot elements. It describes how creep, which is the time-dependent increase in depth under a held load, can be modeled for a variety of materials using Maxwell and Voigt models. Equations are presented that relate the depth increase over time to the elastic modulus and viscosity of the material being tested. A method is described for fitting experimental nanoindentation data, including holding periods, to these equations to determine material properties while accounting for creep. The approach aims to provide an accessible way to analyze creep in nanoindentation that can be incorporated into computer programs.
Process of Nanoindentation and use of finite element modellingD.R. Kartikayan
This document provides an overview of nanoindentation testing for measuring material properties. It discusses why nanoindentation is used, the requirements and procedure for nanoindentation testing, and how to analyze the load-displacement curves obtained from testing. Factors that can affect nanoindentation results are also covered, as well as how finite element modeling can be used to better interpret nanoindentation data and account for these influencing factors.
La nanoindentación es una prueba de dureza que mide las propiedades mecánicas de un material a escala nanométrica mediante el uso de una pequeña punta que indenta la muestra. La carga y desplazamiento se miden continuamente para determinar la dureza y el módulo de Young. Ofrece ventajas como ser rápido, permitir múltiples medidas en una misma muestra, y analizar muestras pequeñas como películas delgadas. Sin embargo, el equipo es muy sensible a vibraciones y cambios térmicos
Nanoindentation is a technique used to determine material properties such as hardness and elastic modulus at small length scales. It works by pressing an indenter with a very small tip into the material and measuring the resulting load and displacement. Factors like thermal drift, machine compliance, and real tip geometry must be accounted for when analyzing the load-displacement data to determine properties. Commercial nanoindentation machines use various methods like capacitive sensing or optical lever systems to precisely measure displacement during indentation testing.
1. Nanoindentation was used to characterize the mechanical properties of various nanostructures such as carbon nanotubes, silver nanowires, and zinc oxide nanobelts.
2. Pressure-induced phase transformations were observed in materials like silicon and germanium during nanoindentation. Pop-in and pop-out events indicated phase changes.
3. Nanoindentation helped determine the mechanical properties of thin films, MEMS structures, and the effects of residual stress. It was also used to study superlattices.
El documento describe diferentes métodos para medir la dureza de los materiales, incluyendo ensayos de rayado, penetración y dinámicos. Explica métodos como Brinell, Vickers, Rockwell, Shore y Knoop, detallando el procedimiento y características de cada uno. El documento provee información sobre cómo medir y comparar la dureza de diferentes materiales.
- QTPIE has become faster and researchers now understand why previously calculated dipole moments and polarizabilities were not translationally invariant or size extensive.
- Researchers have optimized Gaussian type orbitals to closely match Slater type orbitals, resulting in very little error (<0.00001e) in calculations using QTPIE.
- Using sparse matrix data structures and conjugate gradients optimization allows QTPIE to solve problems more efficiently in both memory usage and speed compared to conventional methods.
Elastic Modulus And Residual Stress Of Thin Filmserikgherbert
1. The document proposes a simple model and experimental technique to measure the elastic modulus and residual stress of free-standing thin films using nanoindentation.
2. The technique involves measuring the stiffness-displacement relationship of thin film bridges under an applied load to minimize errors from thermal drift.
3. Experimental tests on aluminum-copper thin films found the elastic modulus was independent of length as expected but residual stress was affected by bending behavior and film thickness. The results validated the proposed model and technique.
The document is a lesson on continuity and infinite limits. It defines infinite limits, including limits approaching positive or negative infinity. It provides examples of evaluating limits at points where a function is not continuous. It also outlines several rules of thumb for manipulating infinite limits, such as the sum or product of an infinite limit with a finite limit being infinite. The document cautions that limits of indeterminate forms like 0×∞ or ∞-∞ require closer examination rather than following rules of thumb. It provides an example of rationalizing an expression to put it in a form where limit laws can be applied.
This document summarizes research on developing an efficient higher-order accurate unstructured finite volume algorithm for inviscid compressible fluid flows. The algorithm uses an ILU preconditioned GMRES method to solve the Euler equations on unstructured meshes. Higher-order solutions of up to fourth-order accuracy were obtained. Results show the third-order solution was 1.3-1.5 times more expensive than second-order, while fourth-order was 3.5-5 times more expensive, demonstrating the efficiency of the higher-order approach. Test cases included supersonic and transonic flows, with results agreeing well with structured solvers.
1) 0! equals 1 based on the algebraic definition of the factorial function and properties of the gamma function.
2) The variance formula s^2 is derived from the definition of variance and using algebraic manipulations to simplify the expression in terms of sums of the data values.
3) It is shown that the sample mean x can be expressed as the population mean x' plus the sum of the standardized deviations from the mean, divided by n.
4) The equations for the slope b and y-intercept a of the linear regression line are derived by taking expectations of both sides of the linear equation and rearranging terms involving sums of the data values.
We examine two ways of extending the definition of limit: A function can be said to have a limit of infinity (or minus infinity) at a point if it grows without bound near that point.
A function can have a limit at a point if values of the function get close to a value as the points get arbitrarily large.
The document discusses mathematical techniques for diffusion magnetic resonance imaging (MRI). It introduces diffusion tensor imaging (DTI) and describes how DTI models water diffusion using a tensor. It then presents equations for calculating the probability of water diffusion over time using the diffusion tensor. Finally, it discusses DTI scale space and describes equations for smoothing diffusion tensors over scale.
Cosmin Crucean: Perturbative QED on de Sitter Universe.SEENET-MTP
The document summarizes key aspects of quantum field theory on de Sitter spacetime, including solutions to the Dirac, scalar, electromagnetic, and other field equations. It presents:
1) Fundamental solutions for the Dirac equation and orthonormalization relations for Dirac spinor modes.
2) Solutions to the Klein-Gordon equation for a scalar field and corresponding orthonormalization relations.
3) Quantization of electromagnetic vector potentials in the Coulomb gauge and orthonormalization relations for photon modes.
This document discusses several basic trigonometric identities involving sines, cosines, and tangents. It provides examples of identities such as:
1) The Pythagorean identity, which states that for all theta, cos^2(θ) + sin^2(θ) = 1.
2) The opposites theorem, which describes trigonometric functions of -θ.
3) The supplements theorem, which relates trigonometric functions of θ to those of π - θ.
It also gives examples of applying various identities to evaluate trigonometric functions and solve trigonometric equations. Homework problems from the text are assigned.
The document discusses seismic design and assessment of masonry structures, focusing on strength evaluation of unreinforced masonry (URM) walls subjected to in-plane forces. It covers topics such as flexural cracking and strength, shear strength criteria including maximum principal tensile stress and Coulomb-like models, and the response of building systems to horizontal loading, highlighting the role of diaphragms, ring beams, and tie rods. Examples of reinforced concrete ring beams are also shown.
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Introducing BoxLang : A new JVM language for productivity and modularity!Ortus Solutions, Corp
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Dynamic. Modular. Productive.
BoxLang redefines development with its dynamic nature, empowering developers to craft expressive and functional code effortlessly. Its modular architecture prioritizes flexibility, allowing for seamless integration into existing ecosystems.
Interoperability at its Core
With 100% interoperability with Java, BoxLang seamlessly bridges the gap between traditional and modern development paradigms, unlocking new possibilities for innovation and collaboration.
Multi-Runtime
From the tiny 2m operating system binary to running on our pure Java web server, CommandBox, Jakarta EE, AWS Lambda, Microsoft Functions, Web Assembly, Android and more. BoxLang has been designed to enhance and adapt according to it's runnable runtime.
The Fusion of Modernity and Tradition
Experience the fusion of modern features inspired by CFML, Node, Ruby, Kotlin, Java, and Clojure, combined with the familiarity of Java bytecode compilation, making BoxLang a language of choice for forward-thinking developers.
Empowering Transition with Transpiler Support
Transitioning from CFML to BoxLang is seamless with our JIT transpiler, facilitating smooth migration and preserving existing code investments.
Unlocking Creativity with IDE Tools
Unleash your creativity with powerful IDE tools tailored for BoxLang, providing an intuitive development experience and streamlining your workflow. Join us as we embark on a journey to redefine JVM development. Welcome to the era of BoxLang.
Getting the Most Out of ScyllaDB Monitoring: ShareChat's TipsScyllaDB
ScyllaDB monitoring provides a lot of useful information. But sometimes it’s not easy to find the root of the problem if something is wrong or even estimate the remaining capacity by the load on the cluster. This talk shares our team's practical tips on: 1) How to find the root of the problem by metrics if ScyllaDB is slow 2) How to interpret the load and plan capacity for the future 3) Compaction strategies and how to choose the right one 4) Important metrics which aren’t available in the default monitoring setup.
From Natural Language to Structured Solr Queries using LLMsSease
This talk draws on experimentation to enable AI applications with Solr. One important use case is to use AI for better accessibility and discoverability of the data: while User eXperience techniques, lexical search improvements, and data harmonization can take organizations to a good level of accessibility, a structural (or “cognitive” gap) remains between the data user needs and the data producer constraints.
That is where AI – and most importantly, Natural Language Processing and Large Language Model techniques – could make a difference. This natural language, conversational engine could facilitate access and usage of the data leveraging the semantics of any data source.
The objective of the presentation is to propose a technical approach and a way forward to achieve this goal.
The key concept is to enable users to express their search queries in natural language, which the LLM then enriches, interprets, and translates into structured queries based on the Solr index’s metadata.
This approach leverages the LLM’s ability to understand the nuances of natural language and the structure of documents within Apache Solr.
The LLM acts as an intermediary agent, offering a transparent experience to users automatically and potentially uncovering relevant documents that conventional search methods might overlook. The presentation will include the results of this experimental work, lessons learned, best practices, and the scope of future work that should improve the approach and make it production-ready.
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[OReilly Superstream] Occupy the Space: A grassroots guide to engineering (an...Jason Yip
The typical problem in product engineering is not bad strategy, so much as “no strategy”. This leads to confusion, lack of motivation, and incoherent action. The next time you look for a strategy and find an empty space, instead of waiting for it to be filled, I will show you how to fill it in yourself. If you’re wrong, it forces a correction. If you’re right, it helps create focus. I’ll share how I’ve approached this in the past, both what works and lessons for what didn’t work so well.
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- QTPIE has become faster and researchers now understand why previously calculated dipole moments and polarizabilities were not translationally invariant or size extensive.
- Researchers have optimized Gaussian type orbitals to closely match Slater type orbitals, resulting in very little error (<0.00001e) in calculations using QTPIE.
- Using sparse matrix data structures and conjugate gradients optimization allows QTPIE to solve problems more efficiently in both memory usage and speed compared to conventional methods.
Elastic Modulus And Residual Stress Of Thin Filmserikgherbert
1. The document proposes a simple model and experimental technique to measure the elastic modulus and residual stress of free-standing thin films using nanoindentation.
2. The technique involves measuring the stiffness-displacement relationship of thin film bridges under an applied load to minimize errors from thermal drift.
3. Experimental tests on aluminum-copper thin films found the elastic modulus was independent of length as expected but residual stress was affected by bending behavior and film thickness. The results validated the proposed model and technique.
The document is a lesson on continuity and infinite limits. It defines infinite limits, including limits approaching positive or negative infinity. It provides examples of evaluating limits at points where a function is not continuous. It also outlines several rules of thumb for manipulating infinite limits, such as the sum or product of an infinite limit with a finite limit being infinite. The document cautions that limits of indeterminate forms like 0×∞ or ∞-∞ require closer examination rather than following rules of thumb. It provides an example of rationalizing an expression to put it in a form where limit laws can be applied.
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1) 0! equals 1 based on the algebraic definition of the factorial function and properties of the gamma function.
2) The variance formula s^2 is derived from the definition of variance and using algebraic manipulations to simplify the expression in terms of sums of the data values.
3) It is shown that the sample mean x can be expressed as the population mean x' plus the sum of the standardized deviations from the mean, divided by n.
4) The equations for the slope b and y-intercept a of the linear regression line are derived by taking expectations of both sides of the linear equation and rearranging terms involving sums of the data values.
We examine two ways of extending the definition of limit: A function can be said to have a limit of infinity (or minus infinity) at a point if it grows without bound near that point.
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The document discusses mathematical techniques for diffusion magnetic resonance imaging (MRI). It introduces diffusion tensor imaging (DTI) and describes how DTI models water diffusion using a tensor. It then presents equations for calculating the probability of water diffusion over time using the diffusion tensor. Finally, it discusses DTI scale space and describes equations for smoothing diffusion tensors over scale.
Cosmin Crucean: Perturbative QED on de Sitter Universe.SEENET-MTP
The document summarizes key aspects of quantum field theory on de Sitter spacetime, including solutions to the Dirac, scalar, electromagnetic, and other field equations. It presents:
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2) Solutions to the Klein-Gordon equation for a scalar field and corresponding orthonormalization relations.
3) Quantization of electromagnetic vector potentials in the Coulomb gauge and orthonormalization relations for photon modes.
This document discusses several basic trigonometric identities involving sines, cosines, and tangents. It provides examples of identities such as:
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2) The opposites theorem, which describes trigonometric functions of -θ.
3) The supplements theorem, which relates trigonometric functions of θ to those of π - θ.
It also gives examples of applying various identities to evaluate trigonometric functions and solve trigonometric equations. Homework problems from the text are assigned.
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Відео та деталі заходу: https://bit.ly/45tILxj
3. MOTIVATION
What we’re after:
– Constitutive behavior of small volumes of viscoelastic solids
subjected time varying excitation over as wide a range of time
or frequency as possible.
Extend the applicability of nanoindentation to
time‐dependent behavior
p
– Flat punch indentation, complex test geometry
– DMA, triple clamp fixture, complex test geometry
– Uniaxial compression simple test geometry
compression, simple test geometry
• Material’s response in the frequency domain ‐ short time
• Material’s response in the time domain ‐ long time
• Bringing them together
• Do it all with flat punch indentation
• Material selection: Highly plasticized PVC
6. MODELING THE INSTRUMENTATION
Nano Indenter® XP:
FREE SPACE
Raw displacement, ± 1 mm
&& &
Fo e iωt = mh + Ch + Kh
h(t ) = ho e i (ωt −φ )
F
K S = o cos φ + mω 2
ho
)
((
−1
)
ho ⎡ ⎤
12
2
= ⎢ K − mω 2 + ω 2C 2 ⎥
F sinφ Fo ⎣ ⎦
C= o
ho ω Cω
tan φ =
K − mω 2
7. MODELING THE INSTRUMENTATION
Nano Indenter® XP:
FREE SPACE
1 degree of
freedom, Z
fd Z
Raw displacement, ± 1 mm
&& &
Fo e iωt = mh + Ch + Kh
h(t ) = ho e i (ωt −φ )
F
K S = o cos φ + mω 2
ho
)
((
−1
)
ho ⎡ ⎤
12
2
= ⎢ K − mω 2 + ω 2C 2 ⎥
F sinφ Fo ⎣ ⎦
C= o
ho ω Cω
tan φ =
K − mω 2
8. MODELING THE INSTRUMENTATION
Nano Indenter® XP:
FREE SPACE
1 degree of
freedom, Z
fd Z
Raw displacement, ± 1 mm
&& &
Fo e iωt = mh + Ch + Kh
h(t ) = ho e i (ωt −φ )
F
K S = o cos φ + mω 2
ho FUNCTION OF
)
((
−1
)
ho ⎡ ⎤
12
2
= ⎢ K − mω 2 + ω 2C 2
POSITION ⎥
F sinφ Fo ⎣ ⎦
C= o
ho ω Cω
tan φ =
K − mω 2
9. Measured stiffness and damping
in free space position = 18 8 μm
space, 18.8
1000
200
ffness, Fo / ho cos φ (N/m)
Dam
mping, Fo / ho si φ (N/
0
800
Measured stiffness
Model
-200
Fo
K s − mω 2 = cos φ 600 FREE SPACE
F
c
ho
-400
400
Fo
Cω = sinφ
ho
400
-600
Measured damping
in
Model
-800
200
-1000
Stif
/m)
0
-1200
1 10
Frequency (Hz)
10. Measured stiffness and damping
in free space position = 18 8 μm
space, 18.8
1000
200
ffness, Fo / ho cos φ (N/m)
Dam
mping, Fo / ho si φ (N/
0
800
Measured stiffness
Model
-200
Fo
K s − mω 2 = cos φ 600 FREE SPACE
F
c
ho
-400
400
Fo
Cω = sinφ
ho
400
-600
Measured damping
in
Model
-800
200
-1000
Stif
/m)
m = 12.15 g
0
-1200
Ks = 95.4 N/m
1 10
C = 2.81 Ns/m
/
Frequency (Hz)
11. ADD THE CONTACT
COUPLED
Fo
cos φ + mω 2
S=
ho
Fo sinφ
C=
ho ω
COUPLED RESPONSE = SAMPLE + INSTRUMENT
⎡F ⎤ ⎡F ⎤
= ⎢ o cos φ + mω 2 ⎥ − ⎢ o cos φ + mω 2 ⎥
K contact
⎢ ho coupled ⎥
⎦ ⎢o inst. (free space) ⎥
h
⎣ ⎣ ⎦
12. PHASOR DIAGRAM: PHYSICAL INSIGHT
Damped, forced oscillator
magina axis (damping, Cω, N/m)
FREE SPACE
,
Fo
Cω = sinφ
ho
Fo
ho Fo
ary
K s − mω 2 = cos φ
ho
φ
Im
Real axis (stiffness, Ks-mω2, N/m)
(stiffness mω
13. PHASOR DIAGRAM: PHYSICAL INSIGHT
Damped, forced oscillator
magina axis (damping, Cω, N/m)
FREE SPACE
,
Fo
Cω = sinφ COUPLED
ho
Fo
ho Fo
ary
K s − mω 2 = cos φ
ho
φ
Im
Real axis (stiffness, Ks-mω2, N/m)
(stiffness mω
14. PHASOR DIAGRAM: PHYSICAL INSIGHT
maginar axis (dampin Ceqω, N/m)
Damped, forced oscillator
FREE SPACE
ω
ng,
Fo
ho
Fo
Ceq ω = sinφ COUPLED
(
ho
Fo
K eq − mω 2 = cos φ
ry
ho
φ
Real axis (stiffness Keq-mω2, N/m)
Im
(stiffness, mω
15. PHASOR DIAGRAM: PHYSICAL INSIGHT
maginar axis (dampin Ceqω, N/m)
Damped, forced oscillator
FREE SPACE
Depends on sample properties and the
p ppp
ω
geometry of the
contact
ng,
Fo
ho
Fo
Ceq ω = sinφ COUPLED
COUPLED
(
ho
Fo
K eq − mω 2 = cos φ
ry
ho
φ
Real axis (stiffness Keq-mω2, N/m)
Im
(stiffness, mω
16. FROM S AND Cω → E’ AND E”
Phasor diagram of Phasor diagram of a linear
Imaginary axis (viscous stres Pa)
mping, Cω N/m)
experimental measurements viscoelastic solid
ss,
E * = E ′ 2 + E ′′ 2
ω,
SAMPLE RESPONSE
SAMPLE RESPONSE
E * = E ′ + iE ′′
Fo
σo
Imaginary axis (dam
ho
E* =
F
Cω = o sinφ εo
ho σo
sinφ
E ′′ =
εo
y
y
σo
Fo
cos φ
S= E′ = cos φ
εo
ho
φ φ
Real i ( tiff
R l axis (stiffness, S N/ )
S, N/m) Real i ( l ti t
R l axis (elastic stress, Pa)
P)
The fundamental equation of nanoindentation:
π1S π 1 Cω
E′ = (1 − ν 2 ) E ′′ = (1 − ν 2 )
2β A 2β A
17. DMA VS. NANOINDENTATION
Highly plasticized polyvinylchloride,
the complex modulus at 22 oC
MPa)
DMA
DMA
1 Nanoindentation
Nanoindentation
10 0.9
odulus (M
punch diameter = 100 μm
Loss Factor (-)
9 0.8
0.7
8
0.6
7
0.5
torage Mo
F
6
0.4
5
0.3
4
St
0.2
3
1 10
1 10
Frequency ( )
q y (Hz)
Frequency (Hz)
q y( )
20. COMPRESSION & INDENTATION
Fo
E′ = cos φ (geometry factor )
ho
10
F
E ′′ = o sinφ (geometry f t ) uniaxial compression
i il i
i t factor 9
ho 1 mm dia. flat punch
8
100 μm dia. flat punch
7
a)
E' (MPa
6
5
Geometry factors:
E
4
L
Compression:
A
FREQUENCY DOMAIN
3
π1 1
(1 − υ 2 )
Indentation:
2β A
0.01 0.1 1 10 100
Frequency (Hz)
21. Fo
E′ = cos φ (geometry factor )
ho
1
F
E ′′ = o sinφ (geometry f t ) uniaxial compression
i t factor
ho 1 mm dia. flat punch
100 μm dia. flat punch
Loss Factor (-)
r
Geometry factors:
0.1
01
L
Compression:
A
FREQUENCY DOMAIN
π1 1
(1 − υ 2 )
Indentation:
2β A
0.01 0.1 1 10 100
Frequency (Hz)
22. Displace
Compression: Indentation:
80
205
ΔL
mN)
P P h
79.6
ε=
σ= σα H = εα
Load On Sample (m
ement Into Surface (μm)
transient response
L
A A D
79.2
200
A ΔL 2Rh(t )
J c (t ) =
D( t ) =
78.8
P (1 − ν 2 )
6 mN step load
LP
O
78.4
78 4
195
10-6
78
77.6
190
2300 2400 2500 2600 2700 2800 2900
Time On Sample (s)
D(t) (m2/N) J (t), flat punch indentation
( ), p
c
-7
(diameter = 983 μm)
10
ε (t )
D( t ) = D(t), uniaxial compression
σo
TIME DOMAIN
10-8
8
10-3 10-2 10-1 100 101 102 103
Creep Time (s)
23. TRANSFORMING FROM FREQUENCY TO TIME
4 term Prony series:
FREQUENCY DOMAIN:
E′
J′ =
E ′2 + E ′′2
4
Ji
J ′ = J0 + ∑
1+ τ i ω 2
2
i =1
TIME DOMAIN:
−t
4
D(t ) = j 0 + ∑ J i (1 − e τ i )
i =1
24. 6
Fo
0.05 Hz Oscillation
E′ = cos φ (geometry factor )
4 1 mm Dia. Flat Punch
ho
Load (mN)
2
Fo
E ′′ = sinφ (geometry factor )
0
ho
-2
L
-7
5x10
-4
FREQUENCY DOMAIN
-6
-7
1200 18003x10
-1800 -1200 -600
1800 1200 600 0 600
Displacement (nm)
2x10‐7
E′
J' (m2/N)
J′ = 2
E ′ + E ′′ 2
-7
1x10 uniaxial compression
Geometry factors:
8x10-8 1 mm dia. mm flat punch
-8
8
L 6x10
Compression:
A
-8
4x10
π1 1
(1 − υ 2 )
Indentation: 0.01 0.1 1 10 100
2β A
Frequency (Hz)
25. J’ (FREQ. DOMAIN) FIT TO PRONY SERIES
FLAT PUNCH INDENTATION
FREQ. DOMAIN:
-7
3.2x10 fit parameters:
E′
τ = 7.5198E-03
J′ =
7 5198E 03
1
E ′2 + E ′′2
2.8x10-7 τ2 = 3.8620E+00
τ3 = 4.1034E-02
fit parameters:
-7
2.4x10 4
J = 3.6960E-08
Ji
J ′ = J0 + ∑
τ4 = 2.9883E-01
0
N)
J' (m2/N
J = 8 2830E 08
8.2830E-08
1+ τ i ω 2
2
-7 1
i =1
2x10 J = 4.6922E-08
2
J = 8.8235E-08
1.6x10-7 3
J = 7.5425E-08
J
4
TIME DOMAIN:
-7
1.2x10
−t
4
D(t ) = j 0 + ∑ J i (1 − e τ i )
-8 nanoindentation data
8x10 4 term parametric model
i =1
curve
c r e fit
-8
4x10
10-2 10-1 100 101 102 103
ω (rad/s)
26. MAXIMIZING THE TIME AND FREQUENCY RANGE
5x10-7
D(t), uniaxial compression,
Combining indentation
-7 measured in the time
3x10 domain data acquired in the
frequency and time
D(t) (m2/N)
0.1
0 .1 domain allows the PVC
= 10 s
= 0.002 s
0.01 H
Hz
50 Hz
reference material to be
-7 characterized over nearly
1x10
8x10-8 6 decades in time (2x10‐3
D
Predicted from flat punch
to 6x102).
-8 nanoindentation data
6x10
acquired in the frequency
domain, 0.01 < f < 50 Hz
4x10-8
-5 -4 -3 -2 -1 0 1 2 3
10 10 10 10 10 10 10 10 10
Creep Time (s)
p ()
27. CONCLUSIONS
* Dynamic nanoindentation of viscoelastic solids requires robust
dynamic characterization of the measurement tool itself, a known
contact geometry, steady‐state harmonic motion, and linear
viscoelasticity.
* In the frequency domain Sneddon’s stiffness equation works
In the frequency domain, Sneddon s stiffness equation works
remarkably well.
* The Prony series model provides a valid path to transition between the
y p p
frequency and time domains.
* It is possible to combine frequency and time domain data from a flat
punch indentation experiment and therefore characterize the sample’s
f ’
behavior over the widest possible range of time and frequency.
28. GEOMETRY OF THE CONTACT
Circular flat punch: Advantages:
– Known contact area
Known contact area
– Area not affected by creep or
thermal drift
Disadvantages:
– Full contact
– Stress concentration
Any tip geometry, consider:
– Steady‐state harmonic motion
– Linear viscoelasticity
Linear viscoelasticity
• Compression distance
• Oscillation amplitude
29. Pre-Compression Dependence
3
3 μm
MPa)
punch dia. = 103 µm
5 μm
10 μm
ulus (M
1 μm
15
Loss F
Storage
20 μm
10
1
ho = 50 nm
Storage Modu
Factor (-)
0.8
0.6
e
0.4
AVG LF (-)
AVG LF (-)
Loss factor AVG LF (-)
S
AVG LF (-)
()
0.2
1
1 10
Frequency (Hz)
F (H )
30. Amplitude Independence
3
MPa)
punch dia. = 103 µm
50 nm
100 nm
ulus (M
500 nm
Loss F
1500 nm
10 3000 nm Storage
1
comp. dist. = 3 µm
p µ
Storage Modu
Factor (-)
0.8
0.6
e
0.4
AVG LF (-)
AVG LF (-)
Loss factor AVG LF (-)
AVG LF (-)
S
AVG LF (-)
0.2
1
1 10
Frequency (Hz)
F (H )