Applied Nanoindentation in Advanced Materials E-Book
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- Herausgeber: John Wiley & Sons
- Kategorie: Fachliteratur
- Sprache: Englisch
Research in the area of nanoindentation has gained significant momentum in recent years, but there are very few books currently available which can educate researchers on the application aspects of this technique in various areas of materials science.
Applied Nanoindentation in Advanced Materials addresses this need and is a comprehensive, self-contained reference covering applied aspects of nanoindentation in advanced materials. With contributions from leading researchers in the field, this book is divided into three parts. Part one covers innovations and analysis, and parts two and three examine the application and evaluation of soft and ceramic-like materials respectively.
Key features:
- A one stop solution for scholars and researchers to learn applied aspects of nanoindentation
- Contains contributions from leading researchers in the field
- Includes the analysis of key properties that can be studied using the nanoindentation technique
- Covers recent innovations
- Includes worked examples
Applied Nanoindentation in Advanced Materials is an ideal reference for researchers and practitioners working in the areas of nanotechnology and nanomechanics, and is also a useful source of information for graduate students in mechanical and materials engineering, and chemistry. This book also contains a wealth of information for scientists and engineers interested in mathematical modelling and simulations related to nanoindentation testing and analysis.
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Seitenzahl: 1355
Veröffentlichungsjahr: 2017
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Table of Contents
Cover
Title Page
Copyright
List of Contributors
Preface
Part I
Chapter 1: Determination of Residual Stresses by Nanoindentation
1.1 Introduction
1.2 Theoretical Background
1.3 Determination of Residual Stresses
References
Chapter 2: Nanomechanical Characterization of Carbon Films
2.1 Introduction
2.2 Factors Influencing Reliable and Comparable Hardness and Elastic Modulus Determination
2.3 Deformation in Indentation Contact
2.4 Nano-scratch Testing
2.5 Impact and Fatigue Resistance of DLC Films Using Nano-impact Testing
2.6 Wear Resistance of Amorphous Carbon Films Using Nano-fretting Testing
2.7 Conclusion
References
Chapter 3: Mechanical Evaluation of Nanocoatings under Extreme Environments for Application in Energy Systems
3.1 Introduction
3.2 Thermal Barrier Coatings
3.3 Nanoindentation Evaluation of Coatings for Nuclear Power Generation Applications
3.4 Conclusions and Outlook
Acknowledgments
References
Chapter 4: Evaluation of the Nanotribological Properties of Thin Films
4.1 Introduction
4.2 Evaluation Methods of Nanotribology
4.3 Nanotribology Evaluation Methods and Examples
4.4 Conclusions
References
Chapter 5: Nanoindentation on Tribological Coatings
5.1 Introduction
5.2 Relevant Properties on Coatings for Tribological Applications
5.3 How can Nanoindentation Help Researchers to Characterize Coatings?
References
Chapter 6: Nanoindentation of Macro-porous Materials for Elastic Modulus and Hardness Determination
6.1 Introduction
6.2 Nanoindentation of Macro-porous Bulk Ceramics
6.3 Nanoindentation of Bone Materials
6.4 Nanoindentation of Macro-porous Films
6.5 Concluding Remarks
Acknowledgements
References
Chapter 7: Nanoindentation Applied to DC Plasma Nitrided Parts
7.1 Introduction
7.2 Basic Aspects of DC Plasma Nitrided Parts
7.3 Basic Aspects of Nanoindentation in Nitrided Surfaces
7.4 Examples of Nanoindentation Applied to DC Plasma Nitrided Parts
7.5 Conclusion
Acknowledgements
References
Chapter 8: Nanomechanical Properties of Defective Surfaces
8.1 Introduction
8.2 Homogeneous and Heterogeneous Dislocation Nucleation
8.3 Surface Steps
8.4 Subsurface Defects
8.5 Rough Surfaces
8.6 Conclusions
Acknowledgements
References
Chapter 9: Viscoelastic and Tribological Behavior of Al2O3 Reinforced Toughened Epoxy Hybrid Nanocomposites
9.1 Introduction
9.2 Experimental
9.3 Conclusion
References
Chapter 10: Nanoindentation of Hybrid Foams
10.1 Introduction
10.2 Sample Material and Preparation
10.3 Nanoindentation Experiments
10.4 Conclusions and Outlook
Acknowledgements
References
Chapter 11: AFM-based Nanoindentation of Cellulosic Fibers
11.1 Introduction
11.2 Experimental
11.3 Mechanical Properties of Cellulose Fibers
11.4 Conclusions and Outlook
Acknowledgments
References
Chapter 12: Evaluation of Mechanical and Tribological Properties of Coatings for Stainless Steel
12.1 Introduction
12.2 Experimental Details
12.3 Results and Discussion
12.4 Conclusions
Acknowledgements
References
Chapter 13: Nanoindentation in Metallic Glasses
13.1 Introduction
13.2 Experimental Studies
13.3 Conclusions
References
Part II
Chapter 14: Molecular Dynamics Modeling of Nanoindentation
14.1 Introduction
14.2 Methods
14.3 Interatomic Potentials
14.4 Elastic Regime
14.5 The Onset of Plasticity
14.6 The Plastic Zone: Dislocation Activity
14.7 Outlook
Acknowledgements
References
Chapter 15: Continuum Modelling and Simulation of Indentation in Transparent Single Crystalline Minerals and Energetic Solids
15.1 Introduction
15.2 Theory: Material Modelling
15.3 Application: Indentation of RDX Single Crystals
15.4 Application: Indentation of Calcite Single Crystals
15.5 Conclusions
Acknowledgements
References
Chapter 16: Nanoindentation Modeling: From Finite Element to Atomistic Simulations
16.1 Introduction
16.2 Scaling and Dimensional Analysis Applied to Indentation Modelling
16.3 Finite Element Simulations of Advanced Materials
16.4 Nucleation and Interaction of Dislocations During Single Crystal Nanoindentaion: Atomistic Simulations
References
Chapter 17: Nanoindentation in silico of Biological Particles
17.1 Introduction
17.2 Computational Methodology of Nanoindentation
in silico
17.3 Biological Particles
17.4 Nanoindentation
in silico
: Probing Reversible Changes in Near-equilibrium Regime
17.5 Application of
in silico
Nanoindentation: Dynamics of Deformation of MT and CCMV
17.6 Concluding Remarks
References
Chapter 18: Modeling and Simulations in Nanoindentation
18.1 Introduction
18.2 Simulations of Nanoindention on Polymers
18.3 Simulations of Nanoindention on Crystals
18.4 Conclusions
Acknowledgments
References
Chapter 19: Nanoindentation of Advanced Ceramics: Applications to ZrO2 Materials
19.1 Introduction
19.2 Indentation Mechanics
19.3 Fracture Toughness
19.4 Coatings
19.5 Issues for Reproducible Results
19.6 Applications of Nanoindentation to Zirconia
19.7 Conclusions
Acknowledgements
References
Chapter 20: FEM Simulation of Nanoindentation
20.1 Introduction
20.2 Indentation of Isotropic Materials
20.3 Indentation of Thin Films
20.4 Indentation of a Hard Phase Embedded in Matrix
References
Chapter 21: Investigations Regarding Plastic Flow Behaviour and Failure Analysis on CrAlN Thin Hard Coatings
21.1 Introduction
21.2 Description of the Method
21.3 Investigations into the CrAlN Coating System
21.4 Concluding Remarks
References
Chapter 22: Scale Invariant Mechanical Surface Optimization
22.1 Introduction
22.2 Theory
22.3 The Procedure
22.4 Discussion by Means of Examples
22.5 Conclusions
Acknowledgements
Referencess
Chapter 23: Modelling and Simulations of Nanoindentation in Single Crystals
23.1 Introduction
23.2 Review of Indentation Modelling
23.3 Crystal Plasticity Modelling of Nanoindentation
23.4 Conclusions
References
Chapter 24: Computer Simulation and Experimental Analysis of Nanoindentation Technique
24.1 Introduction
24.2 Finite Element Simulation for Nanoindentation
24.3 Finite Element Modeling
24.4 Verification of Finite Element Simulation
24.5 Molecular Dynamic Modeling for Nanoindentation
24.6 Results of Molecular Dynamic Simulation
24.7 Conclusions
References
Chapter 25: Atomistic Simulations of Adhesion, Indentation and Wear at the Nanoscale
25.1 Introduction
25.2 Methodologies
25.3 Density Functional Study of Adhesion at the Metal/Ceramic Interfaces
25.4 Molecular Dynamics Simulations of Nanoindentation
25.5 Molecular Dynamics Simulations of Adhesive Wear on the Al-substrate
25.6 Summary and Prospect
Acknowledgments
References
Chapter 26: Multiscale Model for Nanoindentation in Polymer and Polymer Nanocomposites
26.1 Introduction
26.2 Modeling Scheme
26.3 Nanoindentation Test
26.4 Theoretically and Experimentally Determined Result
26.5 Multiscale of Complex Heterogeneous Materials
26.6 Multiscale Modeling for Nanoindentation in Epoxy: EPON 862
26.7 Unified Theory for Multiscale Modeling
26.8 Conclusion
References
Index
End User License Agreement
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Guide
Cover
Table of Contents
Preface
Part I
Begin Reading
List of Illustrations
Chapter 1: Determination of Residual Stresses by Nanoindentation
Figure 1.1 Schematic of the geometry of the cone indentation test.
Figure 1.2 Normalized hardness, as a function of , defined according to Equation (1.1). Schematic of the correlation of sharp indentation testing of elastic-ideally plastic materials as suggested by Johnson [27, 28]. The three levels of indentation responses, I, II and III, are also indicated.
Figure 1.3 Normalized hardness, , and area ratio, , as functions of , defined according to Equation (1.1). Schematic of the correlation of sharp indentation testing of elastic-ideally plastic materials. The three levels of indentation responses, I, II and III, are also indicated.
Figure 1.4 The area ratio, , as function of , defined according to Equation (1.1). Cone indentation of elastic-ideally plastic materials is considered.
Source
: Rydin 2012 [20]. Reproduced with permission of Elsevier.
Figure 1.5 The area ratio, , as function of , defined according to Equation (1.6) with the yield stress replaced by the apparent yield stress in Equation (1.5). Cone indentation of elastic-ideally plastic materials is considered.
Source
: Rydin 2012 [20]. Reproduced with permission of Elsevier.
Figure 1.6 The area ratio, , as function of , defined according to Equation (1.6) with the yield stress replaced by the apparent yield stress in Equation (1.7). Cone indentation of elastic-ideally plastic materials is considered.
Source
: Rydin 2012 [20]. Reproduced with permission of Elsevier.
Figure 1.7 Schematic of the contact area (shaded) at indentation. The principal residual stresses and the corresponding semi-axes of the elliptical contact area are also indicated.
Figure 1.8 Berkovich indentation of an aluminum alloy 8009 (, , MPa (this is the peak stress after a small amount of initial work-hardening), ). The area ratio is shown as function of an applied uniaxial stress (ratio) . (O), experimental results by Tsui
et al.
[11]. (—), theoretical predictions by Larsson [22].
Source
: Larsson 2014. Reproduced with permission of Springer.
Figure 1.9 Semi-axes ratio , see Figure 1.7, as function of the principal stress ratios (horizontal axis) and (vertical axis). Explicit values on are determined by the colors on the right hand side of the Figure The value on the Johnson [27, 28] parameter is .
Source
: Larsson 2012 [23]. Reproduced with permission of Elsevier.
Figure 1.10 Semi-axes ratio , see Figure 1.7, as function of the principal stress ratios (horizontal axis) and (vertical axis). Explicit values on are determined by the colors on the right hand side of the Figure The value on the Johnson [27, 28] parameter is .
Source
: Larsson 2012 [23]. Reproduced with permission of Elsevier.
Chapter 2: Nanomechanical Characterization of Carbon Films
Figure 2.1 Ternary phase diagram of DLC films.
Source:
Robertson 1999 [3]. Reproduced with permision of Cambridge University Press.
Figure 2.2 Contact depth dependence of measured hardness on 60 and 80 nm ta-C films on Si.
Source:
Beake 2010 [28]. Reproduced with permission of Taylor & Francis.
Figure 2.3 Variation in critical load for pop-out with unloading rate on Si (filled symbols) and 80 nm ta-C (open symbols). The peak load was 200 mN for the circles and 100 mN for the triangles.
Figure 2.4 Similarity of loading curves from indentation and scratch tests on a 462 nm ECR-CVD DLC film deposited on Si(100). microns.
Figure 2.5 On-load and residual depth data on Si(100). The linear load ramp started after 50 microns.
Figure 2.6 Nanoindentation and scratch loading curve on Si(100).
Figure 2.7 Influence of probe radius on the critical load for total film failure of 80 nm ta-C film on Si.
Figure 2.8 Influence impact load on behaviour of DLC/Cr on steel.
Figure 2.9 Nano-fretting behaviour of thin DLC films on Si: a) 70 and 80 nm a-C:H films, applied load 10 mN, spheroconical test probe.; b) 150 nm a-C:H film, applied load 1 mN, Berkovich pyramidal test probe.
Figure 2.10 Evolution of friction force as a function of fretting cycles for the three DLC coatings.
Chapter 3: Mechanical Evaluation of Nanocoatings under Extreme Environments for Application in Energy Systems
Figure 3.1 Schematic diagram of the thermal barrier coatings (TBCs). The individual component layers are as shown in the diagram.
Figure 3.2 Schematic representation of influence of residual stress in the load vs depth plot presented by Zhu
et al
.
Figure 3.3 Mechanical properties of YSH and YSHZ coatings measured using nano-indentation.
Figure 3.4 Optical images of YSH and YSHZ coatings after nano-indentation.
Figure 3.5 Mechanical properties of YSH coatings before and after exposure to 1300°C.
Figure 3.6 The changing dose profile (blue), the indentation size effects (red) and effects caused by “contamination” are shown as well as the affected volume of the indentation test presented by Hosemann
et. al
.
Source
: Adapted from Hosemann 2009 [13].
Figure 3.7 Simulation of Au
+3
(5.0MeV) ion distributions and scanning electron microscopy for irradiated and non-irradiated pure W samples.
Figure 3.8 Load vs displacement plot of nanoindentation curve of W-Y sample.
Figure 3.9 Simulation of Au
+3
(5.0 MeV) ion distributions and scanning electron microscopy for irradiated 1e
15
ions/cm
2
and non-irradiated pure W sputtered at 0.43 mbar
−2
.
Chapter 4: Evaluation of the Nanotribological Properties of Thin Films
Figure 4.1 Processing method using an atomic force microscope (AFM).
Figure 4.2 (a) Nanoindentation curve and (b) the dependences of the dissipation modulus on the substrate bias voltage (b) for FCVA-DLC films.
Figure 4.3 Effect of (a) a DC bias voltage and (b) a pulse bias voltage on the nanoindentation hardness (H).
Figure 4.4 Scatter diagram of the modulus of dissipation (E/H) and H for DLC films deposited with 10 different bias voltages.
Figure 4.5 Micro-indentation hardness of a nitrogen-containing carbon film (a) Knoop hardness and (b) Indentation depth.
Figure 4.6 Schematic of the nanowear process.
Figure 4.7 Nanowear profile and histogram of a wear surface (a) Nanowear profile and (b) Histogram of wear surfaces.
Figure 4.8 Scatter diagram of the wear depth and wear volume for DLC films deposited with 10 different bias voltages.
Figure 4.9 Scatter diagram of the wear depth and nanoindentation hardness for DLC films deposited with 10 different bias voltages.
Figure 4.10 Schematic of the ball-on-disk test.
Figure 4.11 Average friction coefficients of DLC films deposited with (a) a DC bias and (b) a pulse bias voltage, lubricated using Z-20 with MoDTC.
Figure 4.12 Average friction coefficient of DLC films deposited with (a) a DC bias and (b) a pulse bias voltage, lubricated with refined water.
Figure 4.13 Wear profiles of DLC films deposited (a) while grounded, (b) with a DC of −100 V and (c) with a pulse bias of −1.0 kV, lubricated using Z-20 with MoDTC.
Figure 4.14 Wear profiles of DLC films deposited (a) while grounded, (b) with a DC of −100 V and (c) with a pulse bias of −1.0 kV, lubricated with water.
Figure 4.15 Scatter diagram of the friction coefficient, nanoindentation hardness and Young's modulus (a) Friction coefficient dependence on nanoindentation hardness in dry condition and (b) Friction coefficient dependence on Young's modulus in dry condition.
Figure 4.16 Vibration nanowear test using an environmentally controlled AFM.
Figure 4.17 Surface profiles after nanowear tests at 200°C under a vacuum (FCVA, load: 4500 nN) (a) Without vibration, (b) Vibration Z and (c) Vibration X.
Figure 4.18 Surface profiles after the nanowear tests at 200°C under a vacuum (ECR, load: 4500 nN) (a) Without vibration, (b) Vibration Z and (c) Vibration X.
Figure 4.19 Torsional displacement of (a) a tip, (b) the locus of the processing tip and (c) Schematic of AFM tip trajectory.
Figure 4.20 AFM image and cross-sectional profiles of the surface topographies obtained at loads of (a) 2100 nN and (b) and 2850 nN. (c) A model of the processed surface of a 2 nm-period film, processed with vibrations.
Figure 4.21 AFM image and cross-sectional profiles of the amplitude at loads of (a) 2100 nN and (b) 2850 nN for a 2 nm-period film, processed with vibrations.
Figure 4.22 Evaluation of the boundary of a nanoperiod multilayer film by force modulation (a) Model of (C/BN)n multilayer film and (b) Relationship between wear depth and friction force.
Figure 4.23 Friction wear tests, performed by applying vertical and lateral vibrations during force modulation (a), (b) Force modulation, (c) Schematic of rectangular pattern trajectory of the AFM tip, showing that the tip applies a vertical vibration in the y direction while scanning the sample in the x direction and (d) Friction wear test.
Figure 4.24 Profile AFM images of (a) the shape of the surface and (b) the phase of a perpendicular magnetic disk substrate after dip coating in a PFPE lubricant, obtained with an AFM over an area of 500 nm
2
.
Figure 4.25 AFM images and section profiles of the amplitudes of disks (a) without and (b) with curing, and (c) the amplitude values as a function of the vibrations, obtained using a LM-FFM.
Figure 4.26 Profile and cross-section of the wear marks of (a) UV-irradiated and (b) untreated PFPE films, obtained with a vibration amplitude of 10 nm.
Figure 4.27 Profile and cross-section of the current distribution of (a) UV-irradiated and (b) untreated PFPE films, obtained with a vibration amplitude of 10 nm.
Figure 4.28 (a) Profile and (b) cross-sectional images of a 4-nm-period (C/BN)n film, obtained at loads of 2500, 3000, 3500 and 4000 nN with a vibration amplitude of 20 nm.
Figure 4.29 (a) Profile and (b) cross-sectional images of the 4-nm-period (C/BN)n topography with a 3500 nN load.
Figure 4.30 (a) Profile and cross-sectional images of the current distribution and (b) a model of the current versus wear track for a 4 nm-period (C/BN)n film with a load of 3500 nN.
Figure 4.31 (a) Profile and cross-sectional images of the friction distribution and (b) a model of the friction versus wear track for a 4 nm period (C/BN)n film with a load of 3500 nN.
Chapter 5: Nanoindentation on Tribological Coatings
Figure 5.1 Multilayered system commonly used in machining inserts for turning or milling operations.
Source
: SANDVIK 2005, Metalcutting Technical Guide [1].
Figure 5.2 Function of each layer in a turning tool insert.
Figure 5.3 Example of a complex multilayered coating system.
Figure 5.4 Multilayered coating system idealized to accommodate polycrystalline diamond on steel substrates (Z1 – Steel substrate, Z2 – Ni Layer, Z3 – Cu Layer and Z4 – Ti Layer).
Source
: Silva 2004 [2]. Reproduced with permission of Elsevier.
Figure 5.5 Multilayered coating used on tool insert for turning operations.
Source
: Adapted from Benes 2007 [3].
Figure 5.6 nanostructured coating used on moulds for injection of reinforced plastics, consisting of successive layers with different density and period of about 43.1 nm.
Source
: Martinho 2011 [4]. Reproduced with permission of American Scientific Publishers.
Figure 5.7 Microindentations performed on titanium nitride [6] smooth film and TiAlSiN rough coating.
Figure 5.8 Different behaviors of the coatings subjected to nanoindentation: (a) hard coating on a soft substrate and (b) soft coating on a hard substrate.
Figure 5.9 Cross-section of a nanoindentation performed with 400 mN using radius spherical indenter on a thick TiN coating deposited on V820 steel substrate.
Source
: MA 2005 [25]. Reproduced with permission of Elsevier.
Figure 5.10 Depth variation during the hold period of 60 seconds at 10% of the maximum load of , caused by thermal drift when testing DLC coatings with 31.4 nm thickness by nanoindentation.
Source
: Chudoba 2001 [28]. Reproduced with permission of Elsevier.
Figure 5.11 Depth variation due to creep effect during the hold time at maximum load of after thermal drift adjustment, when testing DLC coatings with 31.4 nm thickness by nanoindentation.
Source
: Chudoba 2001 [28]. Reproduced with permission of Elsevier.
Figure 5.12 Load-displacement curves corresponding to nanoindentations performed on TiN coatings.
Source
: Weppelmann 1994 [32]. Reproduced with permission of Taylor & Francis.
Figure 5.13 Nanoindentation imprint showing film detachment.
Source
: Abadias 2006 [34]. Reproduced with permission of Elsevier.
Figure 5.14 Load-displacement curves corresponding to nanoindentations performed on TiN coatings.
Source
: Bouzakis 2001[58]. Reproduced with permission of Elsevier.
Chapter 6: Nanoindentation of Macro-porous Materials for Elastic Modulus and Hardness Determination
Figure 6.1 (a) Profile and geometries of sample under loading and unloading with a holding period at peak load
P
max
using a rigid spherical indenter tip with radius of
R
i
; (b) response curve of load versus indent depth and the corresponding geometries. Notice that there is a residual depth h
r
with a cross-sectional profile radius
R
r
.
Figure 6.2 Top surface and cross-sectional SEM images of a SOFC cathode film with a highly porous microstructure.
Figure 6.3 The idealised stress-strain curve for indentation of brittle porous solids, compared with that of a dense solid.
Figure 6.4 Elastic modulus and hardness vs. indentation load for bulk LSCF samples after sintering at 900–1200°C. The solid lines represent extrapolations to zero load.
Figure 6.5 Schematic of half-space cross-sectional view of the effect of separated event of pile-up and sink-in on the actual contact area for nanoindentation on a porous bulk material using a spherical indenter.
Figure 6.6 A typical nanoindentation curve of a highly porous bulk LSCF sample with a porosity of 45%.
Figure 6.7 Elastic modulus measured using nanoindentation on the LSCF film with 40% porosity deposited on a dense CGO substrate.
Figure 6.8 Top surface and cross-sectional SEM images of indents corresponding to maximum indentation depths from 800 to 3600 nm (i.e. 8% <
h
max
/t
f
< 36%), with film being LSCF and substrate being dense CGO.
Figure 6.9 Cross-sectional SEM image of the porous LSCF film after indentation, showing crushing densification zone. Note that in the porous film black is pore and grey is the particle networks.
Figure 6.10 Effect of surface roughness on the real contact area with the indenter tip, leading to errors in indentation results. Here the sample shown was sintered at 1000°C.
Chapter 7: Nanoindentation Applied to DC Plasma Nitrided Parts
Figure 7.1 Schematic representation of the linear glow discharge in abnormal regime, and the potential distribution along the discharge (in red). Also shown is the charge change collision in the cathode sheath.
Figure 7.3 Schematic representation of plasma nitriding for part: (a) acting as cathode (cathode configuration); (b) under floating potential (floating configuration); and (c) acting as anode (anode configuration).
Figure 7.2 Plasma-surface interaction in cathode surface.
Figure 7.4 Different tip-surface approach: a) no asperities present (flat surface); b) asperities larger than tip diameter; c) tip sliding at the asperity; and d) asperity curvature diameter in the same order than tip diameter.
Figure 7.5 (a) Initial portion of the loading curve; and (b) the same curve linearized, for a nanoindentation test of the sample treated at 60% N
2
/40% H
2
atmosphere and 600°C. The arrows indicate the same experimental point in both plots.
Figure 7.6 Instrumented indentation hardness in mechanically polished surface of niobium.
Figure 7.7 Surface aspect of niobium samples nitrided at: a) 500; b) 750; c) 915; and d) 1080°C [23].
Figure 7.8 Roughness profile for surfaces plasma nitrided at: a) 500; and b) 1080°C [23].
Figure 7.9 Hardness of the treated surfaces as a function of the indenter penetration depth for the different studied conditions.
Figure 7.10 (a) Hardness; and b) elastic modulus vs. contact depth for titanium nitrided at 60% N
2
/40% H
2
atmosphere and 800°C: (b) not corrected (as obtained for the nanoindenter algorithm), (c) according to the contact stiffness analysis correction and (d) the Odo-Lepienski method.
Figure 7.11 Hardness vs. contact depth for titanium samples nitrided at 700°C, 800°C and 900°C and 20% N
2
/80% H
2
atmosphere, corrected by the contact stiffness analysis (). Vickers microhardness values are also shown (). The lines are a guide for the eyes.
Chapter 8: Nanomechanical Properties of Defective Surfaces
Figure 8.1 Scheme of a defective surface with some of the possible types of surface defects most frequently encountered. A: surface step, B: surface vacancy, C: adatom, D: sub-surface dislocation, E: vacancy, F: substitutional atom, G: interstitial, H: asperity.
Figure 8.2 Representative force-penetration curves performed at various temperatures on Pt(110). The yield point (where the experimental data deviate from the expected hertzian elastic behavior, black line) decreases with higher temperatures.
Figure 8.3 Scheme of a surface step before (top) and after (bottom) a partial collapse resulting from an applied force. A dislocation half loop is nucleated at the step, and the energy of the step is reduced by Δ
U
STEP
. The former can be described in terms of step line energy γ
L
or step surface energy γ . In any case, Δ
U
STEP
is an energetically favourable term.
Figure 8.4 (Left) Representative force-penetration experimental curves for a flat Au(111) surface (red) and a stepped Au(788) surface (blue). The hertzian fits are shown for both curves, which terminate at point YP at the flat surface and at point A at the stepped surface. (Right) Distribution of termination points YP and A for the flat and stepped surfaces, respectively.
Figure 8.5 (Top) AFM image showing six nanoindentations in a MgO single crystal. The contact points are represented by a purple circle, and those indentations where the plastic yield has been reached show an additional red circle. All the pits correspond to pre-existing dislocations. (Bottom) Load at the yield point versus density of pre-existing dislocations.
Figure 8.6 (Left) Representative force versus penetration curves performed in flat (green) and ion-bombarded (red) Au(100) surfaces. The hertzian fit is also represented, which terminates at the yield point of each surface. (Right) AFM image of a matrix of several nanoindentations (performed with increasing maximum applied load from top to bottom and from left to right) on a Au(100) surface. This surface has been previously nanostructured with low energy ion bombardment at high ion doses and fluxes.
Source
: Rodríguez 2013 [63]. With permission of IOP.
Chapter 9: Viscoelastic and Tribological Behavior of Al2O3 Reinforced Toughened Epoxy Hybrid Nanocomposites
Figure 9.1 Functionalization of alumina particles with GPS.
Figure 9.2 TEM micrograph of (a) nano- Al
2
O
3
and (b) silane-treated nano-Al
2
O
3
.
Figure 9.3 Preparation of C4 e-BMI/DGEBA/Al
2
O
3
nanocomposites.
Figure 9.4 FTIR spectra of C4 e-BMI/Al
2
O
3
-toughened epoxy nanocomposites.
Figure 9.5 The optical surface profile images of (a) neat epoxy, (b) 15 wt% alumina (c) 15 wt% C4 e-BMI/epoxy system/1 wt% GPS-alumina (d) 15 wt% C4 e-BMI/epoxy system/3 wt% GPS (e) 15 wt% C4 e-BMI/epoxy system/5 wt% GPS-alumina C4 e-BMI/epoxy system and (f) 15 wt% C4 e-BMI/epoxy system/10 wt% GPS-alumina.
Figure 9.6 SEM images of C4 e-BMI-toughened epoxy matrices containing (a) 1 wt% GPS, (b) 3 wt% GPS Al
2
O
3,
(c) 5 wt% GPS Al
2
O
3
and (d) 10 wt% GPS Al
2
O
3
.
Figure 9.7 TEM images of C4 e-BMI-toughened epoxy matrices containing (a) 3 wt% GPS Al
2
O
3
, (b) 5 wt% GPS Al
2
O
3
and (c) 10 wt% GPS Al
2
O
3
.
Figure 9.8 Storage modulus of the C4 e-BMI/epoxy/Al
2
O
3
composite systems.
Figure 9.9 Glass transition temperatures of the C4 e-BMI/Al
2
O
3
–toughened epoxy nanocomposite systems.
Figure 9.10 Hardness profile of 15 wt% C4 e-BMI/Al
2
O
3
–toughened epoxy nanocomposite systems.
Figure 9.11 The surface profile across the groove of (a) neat epoxy. (b) 15 wt% C4 e-BMI/epoxy system. (c) 15 wt% C4 e-BMI/epoxy system/1 wt% GPS-functionalized alumina. (d) 15 wt% C4 e-BMI/epoxy system/3 wt% GPS-functionalized alumina. (e) 15 wt% C4 e-BMI/epoxy system/5 wt% GPS-functionalized alumina and (f) 15 wt% C4 e-BMI/epoxy system/10 wt% GPS-functionalized alumina.
Figure 9.12 SEM images of worn surfaces of C4 e-BMI/Al
2
O
3
toughened epoxy nanocomposite systems.
Chapter 10: Nanoindentation of Hybrid Foams
Figure 10.1 The images after polishing the specimen: 2D image using electro microscopy of Ni(a) and Al(c); 3D topography from in situ scanning probe microscopy (SPM) image mode using a Berkovich indenter tip of Ni(b) and Al(d).
Figure 10.2 The loading history using a force controlled mode (a), and the corresponding force-displacement curves of a set of indentation points (b).
Figure 10.3 Indentation pattern (automatic way).
Figure 10.4 Four test lines are chosen on the pre-treated Ni part in nanoindentation with four positions in each line. The distances between the chosen position and the interface boundary are listed on the right-hand side.
Figure 10.5 The measurements of Ni at the test line1 (a, b), line2 (c, d), line3 (e, f), line4 (g, h): load-displacement data (a, c, e, g) and the determined Young's modulus (E-modulus) and hardness (b, d, f, h) on different positions using nanoindentation.
Figure 10.6 Two test lines are chosen on the pre-treated Al part in nanoindentation with four positions in each line. The distances between the chosen position and the interface boundary are listed on the right-hand side.
Figure 10.7 The measurements of Al at the test line1 (a, b) and line2 (c, d): load-displacement data (a, c) and the Young's modulus (E-modulus) and hardness (b, d) on different positions determined by nanoindentation.
Chapter 11: AFM-based Nanoindentation of Cellulosic Fibers
Figure 11.1 Setup to control relative humidity within the AFM's fluid cell as a schematical representation.
Figure 11.2 Schematic of (a) the fluid cell body with connection ports and (b) the body without ports. Both bodies can be operated in (c) the closed and (d) the open configuration.
Figure 11.3 Sketch of the load schedule used for AFM-NI. See text for details.
Figure 11.4 The principle of tip-sample dilation. If the opening angle of the sharp spike is lower than the one of the tip, the resulting image will actually represent the tip.
Figure 11.5 (a) A 3D representation of the 4-sided pyramid tip (ND-DYIRS) and (b) its corresponding area function. The areas represented by quadrilaterals in (a) correspond to the circles with the respective color in (b). A finite tip apex is emphasized by the inset in (a).
Figure 11.6 Resulting 3D shape of a contaminated (a) and cleaned (b) full diamond tip, obtained by scanning across a spike of the TGT01 calibration grid.
Figure 11.7 Schematical illustration of the preparation of (a) dried and (b) wet fibers for AFM-NI.
Figure 11.8 The effect of tip-sample dilation on topography images recorded on pulp fiber surfaces with AFM-NI probes. (a) Schematic illustration and (b) dilation (marked by the shaded areas) on an actual AFM topography image.
Figure 11.9 Hardness (a) and reduced modulus (b) of pulp fibers as a function of relative humidity, determined by using a three-sided pyramidal tip. The data points are averages of 10 to 30 individual indents from one to two fibers.
Figure 11.10 Exemplary plots recorded on (a) classical and (b) flat, rectangular viscose fibers with different modifications incorporated.
Figure 11.11 AFM-NI results of swollen classical viscose fibers as (a) hardness and (b) reduced modulus. The number of averaged indents are given in brackets.
Figure 11.12 AFM-NI results of swollen rectangular viscose fibers as (a) hardness and (b) reduced modulus. The number of averaged indents are given in brackets.
Figure 11.13 Relation of geometrical swelling s
r
to (a) hardness H and (b) reduced modulus of classical viscose fibers.
Figure 11.14 Relation of geometrical swelling s
r
to (a) hardness H and (b) reduced modulus E
r
of rectangular viscose fibers.
Chapter 12: Evaluation of Mechanical and Tribological Properties of Coatings for Stainless Steel
Figure 12.1 XRD patterns of β-TCP/Ch coatings deposited with different chemical compositions. The diffraction patterns show rhombohedral configurations corresponding to β-TCP and also a displacement and widening of the preferential peaks that indicate the compression stress due to the increase in the chitosan percentage.
Figure 12.2 XRD patterns of different β-TCP/Ch coatings: (a). full width at half maximum (FWHM) variations as a function of chitosan percentage change and (b) peak area and peak height changes of preferential peak (0018) as a function of chitosan percentage. The curves show the compression stress effect in crystal structure due to the changes in chitosan percentage; it was evidenced by the decrease of peak area and peak height while the chitosan percentage increased.
Figure 12.3 SEM micrographs of different β-TCP/Ch coatings: (a) β -TCP
100%
/Ch
0%
, (b) β -TCP
95
%/Ch
5
%, (c) β -TCP
90
%/Ch
10
%, (d) β -TCP
90
%/Ch
25
%, (e) β -TCP
65
%/Ch
35
%, and (f) β -TCP
50
%/Ch
50
%. The irregular particles are related with the particles without a defined shape; Particles type needle are elongated particles and angular particles are agglomerated particles with angular shapes.
Figure 12.4 Representative AFM images of β-TCP/Ch coatings on the 316L SS substrates: (a) β-TCP100%/Ch0%; (b) β-TCP95%/Ch5%; (c) β-TCP65%/Ch35%; and (d) β-TCP50%/Ch50% coatings.
Figure 12.5 Morphological analysis of β-TCP/Ch coatings on the 316L SS substrates: (a) Roughness as a function of chitosan percentage curve, and (b) Grain size as a function chitosan percentage.
Figure 12.6 Nanoindentation test results for the β-TCP/Ch coatings: load-displacement indentation curves as a function of increasing the chitosan percentage.
Figure 12.7 Mechanical properties of the β-TCP/Ch coatings: (a) Hardness values of the β-TCP/Ch coatings as a function of chitosan percentage and (b) Elastic modulus of the β-TCP/Ch coatings as a function of chitosan percentage.
Figure 12.8 Mechanical properties: (a) Elastic recovery as a function of chitosan percentage, and (b) Plastic deformation resistance as a function of increasing in the chitosan percentage.
Figure 12.9 Tribological results of the 316L SS substrates coated with β-TCP/Ch coatings: (a) friction coefficient as a function of sliding distance, and (b) friction coefficient as a function of chitosan percentage. The curves explain an inversely proportional relationship between the chitosan amount and friction coefficient.
Figure 12.10 (a-f) SEM micrographs for the wear tracks, evidencing the changes in the wear mechanism (abrasive y adhesive wear) as a function of chitosan percentage for all the β-TCP/Ch coatings.
Figure 12.11 Tribological results for the friction coefficient curves versus the applied load; showing the cohesive (Lc1) and adhesive (Lc2) failure mode for the β-TCP/Ch coatings as a function of increasing in the chitosan percentage.
Figure 12.12 Critical load associated to the adhesion failure (Lc2) as a function of chitosan percentage for all the coatings: (β -TCP100%/Ch0%, β TCP95%/Ch5%, β -TCP90%/Ch10%, β -TCP90%/Ch25%, β -TCP65%/Ch35%, and β -TCP50%/Ch50%).
Chapter 13: Nanoindentation in Metallic Glasses
Figure 13.1 Schematic of indentation of bulk materials.
Figure 13.2 Geometries of indenters used in instrumented indentation.
Figure 13.3 (a) Example of indentation P-h curves for different MGs, showing discrete pop-ins, or flow serration. (b) Example of rate-dependence of serrated flow beneath nanoindenter in Pd-based metallic glass.
Figure 13.4 Schematic of pile-up and sink-in effects in indentation.
Figure 13.5 (a) Pile-up around indenter in MG. (b) Pile-up profile around indenter.
Figure 13.6 Effect of tensile (a) and compressive (b) residual stress on plastic-zone size, pile-up behaviour and shear-band activity.
Figure 13.7 Analysis of hardness data according to the Nix–Gao model: plots of hardness
vs
. penetration depth.
Figure 13.8 Variation in maximum shear stress at first pop-in with tip radius for as-cast and annealed Zr-based metallic glass.
Figure 13.9 Experimental arrangement for indentation test of MG.
Figure 13.10 (a) Geometry of loading-induce impression of radius with a rigid indenter radius . (b) Load- displacement curve for specimen loaded with spherical indenter showing both loading and unloading responses.
Figure 13.11 (a) Roughness micrograph of surface of MG specimen showing roughness less than 5 nm. (b) SEM image of indenter tip with nominal tip radius of 5 µm.
Figure 13.12 Typical load-displacement response of Zr
48
Cu
36
Al
8
Ag
8
at loading rate 0.1 mN/s showing initial deformation.
Figure 13.14 Indentation load-displacement curve of Zr-based MG for incremental loading-unloading at loading rate of 2 mN/s.
Figure 13.13 Indentation load-depth plots for Zr
48
Cu
36
Al
8
Ag
8
under incremental loading-unloading nanoindentation at load rate of 0.1 mN/s.
Figure 13.15 Load-displacement curves for two strain rates. The inset is an enlarged portion showing no creep behaviour.
Figure 13.16 Representative P-h curve for loading rate of 2 mN/s demonstrating discrete serrated flow (The inset shows a conversion from the loading rate to the strain rate.)
Figure 13.17 Typical load-displacement plots for Zr-based MG at loading rate of 0.1 mN/s (a) pure elastic deformation; (b) initial plastic deformation.
Chapter 14: Molecular Dynamics Modeling of Nanoindentation
Figure 14.1 Setup of the simulation system (a) and loading profile (b). The substrate has thermostatting and rigid zones at its boundaries.
Figure 14.2 Control methods for experimental nanoindentation. MD simulations can produce each of the shown pop-ins.
Figure 14.3 Pressure dependence of the elastic constants of Ta for (a) the extended Finnis-Sinclair potential by Dai
et al
. [66], and (b) the EAM potential by Li
et al
. [92].
Source
: Li 2003. Reproduced with permission of American Physical Society.
Figure 14.4 Generalized stacking fault energy. (a) An f.c.c. metal, Cu, shows a stable minimum for . Data obtained for the (111) plane and an EAM potential [68], after [95]. (b) A b.c.c. metal, Ta, does not develop stable stacking faults along the [111] direction. A stacking fault with reproduces the lattice. Data obtained for the (110) plane, after [36]; the extended Finnis-Sinclair potential by Dai
et al
. [66] has been used.
Figure 14.5 Relevant geometrical parameters.
Figure 14.6 Indentation with a rigid atomistic indenter (radius nm, consisting of 57 903 C atoms arranged in a diamond lattice) into a (100) Fe surface with a velocity of 10 m/s. The substrate contains atoms to provide enough space for the development of dislocations. Substrate temperature was set to 0 K to ease detection of lattice defects. In the load-displacement curve (a) several points are marked. These are shown successively in (b)–(e). Yellow: deformed surface including unidentified defects. Dislocation lines with Burgers vector are shown in red, those with in blue. Green arrows indicate direction of . Dislocations are detected using the DXA algorithm [103]. Visualization has been prepared using Paraview [104].
Figure 14.7 Indentation velocity dependence of the load-displacement curves for a typical MD simulation. As the penetration rate decreases, the first pop-in event becomes more noticeable, with a marked reduction in load at the onset of plasticity. Arrows indicate the first pop-in events for the two indentation velocities explored.
Figure 14.8 Indenter-size dependence of the loading curves for a Ta (100) defect-free single crystal. The legend indicates the radius of the spherical tip used for the simulations, using an indenter velocity of 34 m/s.
Figure 14.9 Indentation of a rigid atomistic indenter (radius R=2.14 nm, consisting of 7248 C atoms arranged in a diamond lattice) into a (110) Cu surface with a velocity of 20 m/s at 0 K. The substrate contains 4.1 x 10
16
atoms; only the zone close to the indenter is shown. Between the indentation depth of (a) 21.0 Å and (b) 21.4 Å, a prismatic loop detaches from the complex dislocation network developing under the indenter. Yellow: deformed surface including unidentified defects. Dislocation lines with Burgers vector are shown in red, those with in blue. Green arrows indicate direction of . Dark green areas denote stacking faults. Dislocations are detected using the DXA algorithm [103]. Visualization has been prepared using Paraview [104].
Figure 14.10 Example of the ‘lasso’ mechanism as proposed by Remington and co-workers [37]. The process of prismatic loop formation along the {111} direction can be seen in this sequence (a) - (d): the shear loops nucleated during the indentation process expand into the material by the advancement of their edge components, while screw components of the loop cross-slip. As they approach they annihilate to produce prismatic loops. MD nanoindentation simulation of (100) Ta at 300 K using an indenter size of8 nm radius and a penetration velocity of 34 m/s.
Figure 14.11 Radial dislocation density profile for Ta (100) using an extended Finnis-Sinclair potential and a 20 nm diameter indenter. The increase near 25 nm is due to the presence of detached prismatic loops.
Figure 14.12 Topography of imprints produced by a 16 nm diameter indenter on the three simply indexed Ta surfaces. Gray-scale bar shows pile-up height in nm. (a) Ta (100), (b) Ta (110), (c) Ta (111).
Figure 14.13 Specimen is indented by a rigid spherical indenter, producing an arrangement of circular loops of GNDs during the process. The slope of the pit profile can be related to the separation between slip events and the Burgers vector of the dislocations.
Chapter 15: Continuum Modelling and Simulation of Indentation in Transparent Single Crystalline Minerals and Energetic Solids
Figure 15.1 Polycrystal with binder (left, PBX-9404) and single crystals (right, 1 cm grid) [courtesy D. Hooks, LANL].
Figure 15.2 Predicted force-displacement curves [17] obtained using soft [35] and stiff [36] elastic constants compared with experimental load excursion data [29] (left) and total slip for indentation depth of 200 nm (right).
Figure 15.3 Force-displacement predictions from various elastic constants [34–36] compared to experiment [29] (left) and predicted pressures for indentation depth of 200 nm (right) onto (001), (021), and (210) faces of RDX.
Figure 15.4 Comparison of AFM deflection image from experiment [29] (left) and predicted residual total cumulative slip (right) upon unloading of (021) face of RDX crystal. Left Figure reprinted from Figure 7 of reference [29].
Source
: Ramos 2009 [29]. Reproduced with permission from Taylor & Francis Ltd.
Figure 15.5 Indentation experiments on (100) cleavage plane of calcite: 3 mm diameter diamond indenter [43].
Figure 15.6 Wedge indentation in calcite: geometry (left), nonlinear prediction (center), linear prediction (right).
Source
: Clayton 2011 [18]. Reproduced with permission of IOP.
Figure 15.7 Nonlinear anisotropic elastic model predictions of resolved shear stress for twinning in calcite.
Figure 15.8 Twin morphology: spherical indenter of diameter 2
R
, indentation depth
D
of 0.013 mm (right).
Figure 15.9 Comparison of present phase field simulation results with analytical solution [11] and experiments [43, 64]: force versus depth (left) and twin length versus force (right).
Chapter 16: Nanoindentation Modeling: From Finite Element to Atomistic Simulations
Figure 16.1 Schematic drawing showing geometric similarity.
Figure 16.2 Surface SEM image of a Ni-porous sample obtained through electrodeposition.
Figure 16.3 Example of a FE mesh for a porous material including pores as spherical cavities on the sketch of the model. Part (a) shows the general perspective with 726 pores, (b) is a cross section showing the inner cavities and (c) shows the same cross-section as in (b) after indenting with a Berkovich indenter, one can observe how the pore (cavity) size is reduced, which will lead to an evolution for the mechanical behaviour of the specimen when compared with its bulk counterpart.
Figure 16.4 (a) High resolution radiographs of the cylindrical porous titanium implants in the condyles of the distal femur after 6 weeks in situ. (b) Micro-CT 3D reconstruction of one of the implants from a in the condyle of the distal femur (asterisked in (a), implant white, bone brown in (b)). (c) 3D visualization of the implant in situ. Part of the bone has been digitally removed to illustrate the trabecular architecture surrounding the implant. Compared to 2D radiographs, 3D reconstructions provide enhanced information regarding implant position and architecture of the surrounding osseous.
Figure 16.5 Diagram showing the von Mises and Tresca yield surfaces for different friction angles associated to DP and MC criteria respectively. Adapted from [22].
Figure 16.6 Schematic drawing of the contact between the indenter and the nanowire. The ‘ideal’ Berkovich indenter is depicted here as an equivalent conical tip with an effective cone angle of 70.3° [24, 6]. The ‘real’ (i.e., blunted) indenter tip, represented with a continuous black line, is more similar to a spherical tip with a radius of 250 nm. The dimensions of the nanowire and the tip are drawn to scale. The contour of the cono-spherical indenter that best approaches the real tip used in our study is drawn in cyan.
Chapter 17: Nanoindentation in silico of Biological Particles
Figure 17.1 Coarse-graining procedure for constructing a self-organized polymer (SOP) model [10, 11] of a polypeptide chain.
Panel A
exemplifies coarse-graining of the atomic structure of the αβ-tubulin dimer – the structural unit of the microtubule cylinder (see Figure 17.3). The amino acid residues are replaced by single interaction centers (spherical beads) with the coordinates of the C
α
-atoms (represented by the black circles). Four representative circles are shown to exemplify the coarse-graining process. Consequently, the protein backbone is replaced by a collection of the C
α
-C
α
covalent bonds with the bond distance of 3.8 Å. The potential energy function (molecular force field) given by Equation (17.1) describes: the binary interactions between amino acids stabilizing the native folded state of the protein, chain collectivity, chain elongation due to stretching, and chain self-avoidance (Equations (15.2)–(15.4)). Because the SOP model is based on the native topology of a particle, the coarse-graining procedure preserves the secondary structure of a protein: α-helices (shown in blue), β-strands and sheets (shown in purple), and random coil and turns (shown in gray).
Panel B
depicts the results of coarse-graining of a small fragment of microtubule cylinder. Four identical copies of the tubulin dimer structure, coarse-grained as described in panel
A,
form a C
α
-based model of the fragment. These are combined together to form a coarse-grained reconstruction of the full microtubule lattice (see Figure 17.3).
Figure 17.3 Dynamic force experiment
in silico
on a fragment of the microtubule cylinder. The particle is immobilized on the substrate surface. The cantilever base (virtual sphere in simulations or piezo- in AFM) is moving in the direction perpendicular to the particle surface described by the cantilever coordinate
Z
with constant velocity
v
f
. This dynamic force-ramp creates a compressive force, which is transmitted to the cantilever tip (sphere of radius
R
tip
) through the harmonic spring with the spring constant κ. The compressive force (with large vertical arrow) ramps up linearly in magnitude with time,
f(t) = r
f
t
, with the force-loading rate
r
f
= κ
v
f
. The force loads the particle and produces an indentation in the particle's structure quantified by the coordinate
X.
The mechanical response, i.e. the restoring force from the particle, is measured by profiling the deformation force (indentation force)
F
as a function of the cantilever base displacement
Z
(
FZ
curve) or as a function of the indentation depth
X
(
FX
curve).
Figure 17.2 Computational acceleration on a GPU for the SOP-GPU software package. Compared is the computational time on a Central Processing Unit (CPU) vs. Graphics Processing Unit (GPU) as a function of the system size (total number of residues)
N
tot
on a logarithmic scale. To perform these comparative benchmark tests, we used a system of
N
tot
independent Brownian oscillators (i.e. uncoupled harmonic oscillators in a stochastic thermostat) at room temperature. We compared the computational performance of the SOP-GPU program on a single GPU device – GeForce GTX 780 (from NVidia) versus 1 CPU core, 6 CPU cores, and 12 CPU cores (Intel Ivy Bridge architecture). We see a substantial computational acceleration when SOP-GPU is used. This acceleration gradually increases with system size, i.e. ∼5–40-fold speedup for
N
tot
≈ 10
5
particles and ∼15–50-fold for
N
tot
≈ 10
6
particles, when the GPU device becomes fully loaded with computational tasks.
Figure 17.4 The crystal structure of the Cowpea Chlorotic Mottle Virus (CCMV) from VIPERdb (PDB entry: 1CWP). Shown is the side view of CCMV; the protein domains forming the pentamer capsomers are coloured in blue, while the same protein domains in the hexamer capsomers are shown in red and orange. The pentamer and hexamer capsomers composed of five and six copies of the same monomer protein domain (circled in the black ellipse), respectively, are magnified on the right. There are small openings in the centers of the pentamer and hexamer capsomers, which correspond to the 5- and 3-fold symmetry axes. The CCMV capsid is a thick shell. The outer diameter of the CCMV shell is ∼26 nm and the shell thickness is ∼2.8 nm; hence, the shell thickness is not negligibly small compared to the shell size. The top structure displays the top view of the CCMV particle with the 2-fold symmetry axis at the center of the common edge of adjacent hexamer subunits.
Figure 17.5 Reversibility of bonds' dissociation in MT protofilament PF8/1. The
FX
curve is obtained with
v
f
= 0. µm/s and
R
tip
= 5 nm. In the forward indentation (structural snapshots 1–3), the tip deforms the protofilament and disrupts the longitudinal bond. The asterisks mark
X
= 7.0 nm (blue), 8.0 nm (green), 8.5 nm (orange), and 9.2 nm (red) deformations corresponding to the fully dissociated state. These were used as initial structures in the subsequent tip retraction simulations.
The inset
shows the structure overlap χ vs. time, which captures dissociation (drop in χ) and subsequent reformation (increase in χ) of the bond between 4-th and 5-th dimers. Snapshots 4–7 obtained from the initial structure corresponding to 8.5 nm deformation (orange asterisk) show the dynamics of bond reformation and protofilament restructuring.
Figure 17.6 Dependence of the forced deformation for single protofilament fragment PF24/1 on the cantilever velocity
v
f
(
R
tip
= 5 nm). Shown in different color are the
FX
curves obtained using different values of
v
f
accumulated in
the table inset
. The horizontal arrows mark the longitudinal bond dissociation transitions which occur at the critical force
F
*
and critical deformation
X
*
.
The inset
also lists the obtained values of
F
*
,
X
*
and the values of deformation work
w
as a function of velocity
v
f
.
Figure 17.7 Force-deformation spectra for single protofilament fragment of the MT PF8/1. Shown are the examples of the force spectra (
FX
curves) for PF8/1 (green and red solid curves) obtained by using the cantilever velocity
v
f
=
0.2 µm/s and tip radius
R
tip
= 10 nm. Structures numbered 1–3, which show the deformation progress, correspond to the green
FX
curve and represent the native state (
X
= 0), weakly bent state (
X
= 2 nm), and dissociated state (
X
= 6 nm), respectively. The tip shown with the vertical arrow deforms the protofilament until the dissociation of the longitudinal bond occurs.
The inset
shows the corresponding profiles of bending energy as a function of deformation for the estimation of the flexural rigidity. The dashed green curve is a fit of the quadratic function to the green curve of the potential energy of deformation
V
vs.
X
, which shows the validity of the harmonic approximation in the calculation of flexural rigidity and persistence length for the protofilament fragments PF8/1, PF16/1, PF24/1, and PF32/1.
Figure 17.8 Force-deformation spectra for 8-dimer fragment of the MT cylinder MT8/13 and for CCMV capsid. The structures of the MT cylinder particle and CCMV spherical particle are presented, respectively, in Figure 17.3 and 17.4. Panels A-C: The force-deformation curves for 7 indentation points on the outer surface of MT lattice (shown in panel A), each depicted with different color, obtained with
v
f
=
1.0 µm/s and
R
tip
= 10 nm. Solid curves and dashed red curves represent the
FZ
profiles (panel A) and
FX
curves (panel B) for the forward deformation and backward tip retraction simulations, which followed the forward indentations (solid red curve) with
Z
= 17, 24, and 35 nm and
X
= 7, 11, 21 nm as initial conditions. Panel C shows the MT structure snapshots 1, 2a, 2b, and 3 illustrating the mechanism of MT deformation and collapse (direction of motion of the cantilever tip is indicated by a large vertical arrow). Structure 1: continuous deformation (
Z
< 15–20 nm,
X
< 6–8 nm; elastic regime). Structures 2a and 2b: disruption of lateral and longitudinal interfaces, respectively (20–25 nm <
Z
< 25–30 nm, 6–8 nm <
X
< 11–13 nm; transition regime). Structure 3: post-collapse evolution (
Z
> 25–30 nm,
X
> 11–13 nm). These structures correspond to the accordingly numbered regions in the
FZ
and
FX
curves in panels A and B. Panels D–F: The force-deformation curves for the CCMV shell indented along the 2-fold, 3-fold, and 5-fold symmetry axis (shown in panel D), each depicted with different color, obtained using
v
f
=
1.0 µm/s and
R
tip
= 20 nm. The force-deformation spectra, i.e. the
FZ
curves (panel D) and
FX
curves (panel E), results for the forward deformation and backward retraction are represented by the solid and dashed red curves, respectively. The retraction simulations are performed using the structures of the deformed CCMV shell occurring at
X
= 5, 11 and 19 nm deformation. The retraction curves show that the 5 nm deformation can be retraced back almost reversibly (small hysteresis), whereas the 19 nm deformation is nearly irreversible (large hysteresis). Panel F shows the CCMV structures numbered 1–3 for the native state of intact CCMV shell (structure 1), for the strongly deformed virus shell right before the transition to the collapsed state occurs (structure 2), and for the globally collapsed state (structure 3).
Figure 17.9 Structure changes observed during mechanical compression of MT cylinder MT8/13. Panel A: MT lattice profile viewed along the cylinder axis for different extent of indentation obtained with
R
tip
= 15 nm (indentation point 7; see Figure 17.8a). The cantilever tip is represented by a sphere. Panel B shows top views of the MT lattice for indentation points 3 (upper raw in B) and 6 (lower raw in B). In the course of mechanical compression (indicated by an arrow in panel A), the MT structure (light blue) is deformed which increases the MT-tip contact area (encircled dark blue area). Subsequent force increase results in the dissociation of lateral tubulin-tubulin bonds and then longitudinal bonds. In panel B, the tubulin monomers with disrupted lateral and/or longitudinal interface(s) are shown in dark red.
Figure 17.10 Force-indentation spectra for the forward indentation and backward (tip) retraction of the MT lattice MT8/13
in silico
and corresponding structure alterations (cantilever velocity
v
f
=
1.0 µm/s and tip radius
R
tip
= 10 nm). Shown are results for the indentation points 2 (green) and 3 (red) in panels A and B, respectively, and for the indentation points 7 (green) and 6 (red) in panels C and D, respectively. Panels A and C: The
FX
curves for forward indentation (solid green and red curves). Curves for the backward tip retraction (dashed red lines) were generated using the structures with
X
= 7, 11, and 21 nm deformation (indicated on the graphs).
The insets
show the profiles of Δ
H
(dashed),
T
Δ
S
(solid) and Δ
G
(dash-dotted) vs.
X
. Panels B and D: The slope of the
FX
curves - the derivative d
F/
d
X
of the curves presented in panels A and C. Snapshots show the side-views of the MT before dissociation of the lateral bonds and after dissociation of the longitudinal bonds.
The insets
show the profiles of χ vs.
X
demonstrating that the MT in the collapsed state (
X
> 20 nm) is ∼80–85% similar to the native undeformed state (
X
= 0).
Figure 17.11 Panels A and B: Nanoindentation
in silico
of the CCMV particle. Show in red and blue color are two representative trajectories obtained for 2-fold symmetry axis (
v
f
= 1.0 µm/s and
R
tip
= 20 nm). Panel A: The force-deformation spectra (
FX
curves); results for the forward deformation and backward retraction are represented by the solid and dotted red curves, respectively. The retraction simulations are performed using the structures of the deformed CCMV shell with
X
= 5 and 11 nm. The dashed line represents the fit to the
FX
curve in the elastic regime (
X
< 3–5 nm) by the nonlinear function ∼
X
3/2
. Structures on the left show the increasing tip-capsid surface contact area (blackened); the structure on the right shows the CCMV profile in the collapsed state.
The inset
is the profile of the structure overlap χ
(X)
, which decreases with indentation
X
. The structure in
the inset
is the CCMV particle before the transition to the collapsed state (
X
≈ 10 nm indentation). Panel B: The profiles of Δ
H
, Δ
G
, and
T
Δ
S
. Also shown are the profile views of CCMV in the elastic deformation regime, where Δ
H
≈
T
Δ
S
, and in the plastic regime, where Δ
H
>
T
Δ
S
.
The inset
shows the profile of the slope of the
FX
curve, i.e. d
F/
d
X
versus
X
, with two peaks which correspond to the mechanically activated (transition) states for the two types of transitions: (i) local curvature change in the tip-capsid surface contact area (first peak at
X
≈ 3 nm and the corresponding top view of CCMV); and (ii) bending deformation of the side portions of CCMV shell (second peak at
X
≈ 7 nm and the corresponding side view of CCMV). Panel C: Surface map of the potential energy (color scale for
U
SOP
is in the graph) for four representative structures of the CCMV shell (top view) observed at
X
= 0, 5 nm, 7 nm, and 16 nm deformation. The direction of motion of the tip is perpendicular to the CCMV surface as indicated by the black cross. The map shows a gradual increase in the potential energy of proteins in pentamers and hexamers as global changes to the structure occur.
Chapter 18: Modeling and Simulations in Nanoindentation
Figure 18.1 The structure of a POSS-PE molecule.
Figure 18.2 (a) The simulation models for the nanoindentation of PE with indenter tips of cube-corner, sphere and flat. (b) The simulation models for the nanoindentation of POSS-PE with indenter tips of cube-corner, sphere and column.
Figure 18.3 The loading and unloading load-displacement curves for (a) PE and (b) POSS-PE under different indenters.
Figure 18.4 The projected hardness for (a) PE and (b) POSS-PE in different indentation simulations.
Figure 18.5 The Martens hardness for (a) PE and (b) POSS-PE in different indentation simulations.
Figure 18.6 The hemisphere area beneath the indenter tip.
Figure 18.7 The average displacements for PE and POSS-PE at different hemisphere radius.
Figure 18.8 Stress distribution in PE at different loadings (only the atoms with stress over 1.5 GPa are displayed).
Figure 18.9 The slipping energy and the indention load for (a) PE and (b) POSS-PE under a cube-corner indenter at each step.
Figure 18.10 The average slipping energy for PE and POSS-PE in the cube-corner nanoindentation simulations.
Figure 18.11 The models of the nanoindentation on nickel with (a) flat-ended, (b) tilted flat-ended, and (c) wedged indenters.
Figure 18.12 The load-displacement curves for the nanoindentation into the (–110) plane of nickel with different indenters. (a) flat-ended, (b) tilted flat-ended, and (c) wedged.
Figure 18.13 The inner structure of nickel beneath the flat-ended indenter at the load depth of (a) 6.8 Å, and (b)(c) 9.2 Å (the dotted lines locate the positions of slip planes, and dimensions and displacements in Å, the same hereafter).
Figure 18.14 Dislocated structures beneath the tilted flat-ended indenter with the inclined angle of (a) 5° (at the load depth of 4.7 Å), (b) 15° (at the load depth of 5.0 Å), and (c) 30° (at the load depth of 4.4 Å).
Figure 18.15 Atomistic structures beneath the wedged indenter with vertex angle of (a) 120° (at the load depth of 6.4 Å), (b) 140° (at the load depth of 7.8 Å) and (c) 160° (at the load depth of 10 Å).
Figure 18.16 The elastic models of the three indentation simulations with (a) flat-ended, (b) tilted flat-ended, and (c) wedged indenters.
Figure 18.17 The shear stresses at different inclined angles as determined from
a
/
a
0
in the tilted flat-ended model. The dotted line locates the position of τ
max
.
Figure 18.18 The shear stresses at different half vertex angles as determined from
a
/
a
0
in the wedged model. The dotted line locates the position of τ
max
.
Chapter 19: Nanoindentation of Advanced Ceramics: Applications to ZrO2 Materials
Figure 19.1 Effect of pore shape and porosity content on elastic modulus.
Figure 19.2 AFM topographic images (3D view) of residual Nanoindentation imprint performed until 300 nm in duplex samples. (a) cubic grain, and (b) boundary between a cubic and several tetragonal grains. Reproduced with permissions from reference.
Figure 19.3 Young's modulus against the indentation depth for 3Y-TZP specimens degraded for 5, 10 and 15 h at 134°C. The solid line represents the fitting of the experimental data using the Bec model [79] in order to determine the degraded layer.
Figure 19.4 Relative hardness cartography superimposed to the scanning electron image showing the indentation array in front of the 3Y-TZP notch.
Chapter 20: FEM Simulation of Nanoindentation
Figure 20.1 Schematic illustration of indentation in an isotropic elasto-plastic material by a self-similar rigid indenter.
Figure 20.2 Schematic illustration of the loading curve for a self-similar indenter and its analytical description by Kick's law.
Figure 20.3 Stress and strain field of materials 1–4. a) The von Mises stress field σ
v
is equal for materials 1 and 2 as well as materials 3 and 4, respectively; b) The plastic equivalent strain field is equal in size, shape, and quantity for materials 1 and 2 as well as materials 3 and 4, respectively.
Figure 20.4 Strain profile of materials 1-4 along the path (x-direction, see Figure 20.3): a) Profile of the ratio between von Mises stress σ
v
and Young's modulus
E
. b) Profile of plastic equivalent strain ϵ
peeq
.
Figure 20.5 Surface profile at maximum indentation depth (3.5 µm). Materials 1 and 2 show pile-up and materials 3 and 4 sink-in behaviour. Materials with constant ratio show identical surface profiles, including equal contact depth
h
c
.
Figure 20.6 Schematic illustration of the indentation of a thin film on a substrate.
Figure 20.7 Plastic strain distribution of the film-substrate system: a) hard film on soft substrate. b) soft film on hard substrate.
