High resolution study of local stress inside alumina [Elektronische Ressource] : micro mechanical analysis using laser scanning confocal microscope / Yun Chen

Yun Chen

Sujets

• Physik

Informations

• Publié par: johannes_gutenberg-universitat_mainz
• Publié le: 01 janvier 2008
• Nombre de lectures: 21
• Langue: Deutsch
• Poids de l'ouvrage: 3 Mo

Extrait

High resolution study of local stress inside
alumina - Micro Mechanical Analysis Using Laser
Scanning Confocal Microscope



Dissertation
zur Erlangung des Grades
„Doktor der Naturwissenschaften“


am Fachbereich Chemie, Pharmazie und Geowissenschaften
der Johannes Gutenberg-Universität Mainz






Yun Chen
geb. in Wuxi, P. R. China


Mainz 2007



Dekan: Uni.-Prof . Dr. P. Langguth

Erster Berichterstatter: Prof. Dr. H.-J. Butt
Zwiter Berichterstatter: Prof. Dr. T. Basche
Tag der mündlichen Prüfung: den 18. Dezember 2007


























Die vorliegende Arbeit wurde in der Zeit von October 2005 bis September 2007
am Max-Planck-Institut für Polymerforschung
unter der Betreuung von Herrn Prof. Dr. H.-J. Butt angefertigt.





Contents:

Abstract..........................................................................................................................3
Symbols and abbreviations ............................................................................................5
1. Introduction................................................................................................................7
1.1 Mechanical contact...............................................................................................7
1.2 Theoretical aspects for stress analysis..................................................................8
1.2.1 Analytical formulation ...................................................................................8
1.2.2 Numerical simulation12
1.3 Experimental stress analysis...............................................................................13
1.3.1 Strength test .................................................................................................13
1.3.2 Photoelasticity photography.........................................................................15
1.3.3 Fatigue tests by impact and micro indentation ............................................17
1.3.4 Fluorescence and Raman spectroscopy .......................................................18
1.4 Ruby – stress sensitive material .........................................................................19
1.4.1 General properties........................................................................................19
1.4.2 Pressure gauge for hydrostatic environment................................................21
1.4.3 Spectral shift under non-hydrostatic environment.......................................21
1.4.4 Brittleness and ductility ...............................................................................22
1.5 Laser scanning confocal microscopy .................................................................23
1.6 One vs. two-photon excitation............................................................................25
2. Materials and methods .............................................................................................27
2.1 Materials.............................................................................................................27
2.2 Instruments .........................................................................................................28
2.3 Setup...................................................................................................................29
2.4 Numerical simulations by FEM .........................................................................30
2.5 Experimental procedures....................................................................................31
2.6 Data analysis - determination of conversion factor............................................33
3. Results and discussion .............................................................................................36
3.1 Calculation of stress by simulations...................................................................36
13.2 Defocusing effect and refractive index matching...............................................39
3.3 Ruby fluorescence spectra and spectral shift under stress .................................45
3.4 General stress distribution within the ruby sphere .............................................47
3.5 Stress distribution at the microcontact ...............................................................52
3.6 Quasi-static compression and stress development57
3.7 Two-photon excitation........................................................................................63
3.8 Repeated loading cycles .....................................................................................67
3.9 Periodic loading using piezo vibration...............................................................77
4. Summary and conclusion.........................................................................................86

Bibliography ................................................................................................................89
Acknowledgement .......................................................................................................98
Curriculum Vitae........................................................................................................100
























2Abstract
The aim of this work is to measure stress in a micro sphere of hard materials
subjected to uniaxial loads applied by two rigid plates and to compare it to theoretical
predictions. I described to my knowledge the first direct measurement of stress at a
mechanical microcontact. To measure the internal stress distribution, I compressed
3+ruby spheres (α-Al O : Cr , 150 μm diameter) between two sapphire (α-Al O ) plates. 2 3 2 3
Ruby shows a fluorescence spectrum when being excited. The fluorescence spectrum
peaks at 694.3 nm (R line) and 692.8 nm (R line). It played the role of a stress sensor. 1 2
The peaks shift to longer wavelengths under compression and the distance of shift can
be related to stress by a proper conversion coefficient. Since the ruby sphere is
transparent and polished to optical level, fluorescence spectra can be obtained from
inside the sphere. Thus a laser scanning confocal microscope was used to excite
fluorescence at any positions inside the ruby sphere with spatial resolution of about
31×1×1 μm . Figure 1 shows the scheme of the experimental setup.

Fig. 1. Schematic sketch of the experimental setup.

Under static external loading forces, the stress distribution within the center
plane of the ruby sphere was measured directly for the first time and compared to
Hertz’s law. The measurement was in good agreement with theoretical prediction as
well as the FEM simulations. The stress across the contact area showed a
hemispherical profile. The measured contact radius was in accord with the value
3calculated by Hertz’s equation.
By stepwise increasing of load, stress-vs-force curves were obtained and used
to analyze the stress development at the contact region. The results showed spike-like
decrease of stress after entering non-elastic phase. This was attributed to the formation
and coalescence of microcracks, which led to relaxing of stress. In the vicinity of the
contact area luminescence spectra with multiple peaks were observed. This indicates
the presence of regions of different stress, which are mechanically decoupled.
Repeated loading cycles were used to study the fatigue of ruby at the contact
region. Progressive fatigue was observed when the load exceeded the lower limit of
the critical load. As long as the load did not exceed the critical load of yield
stress-vs-load curves were still continuous and could be described by Hertz’s law with
a reduced Young’s modulus. Once the load exceeded the critical load, spike-like
decreases of the stress could be observed.
Vibration loading with higher frequencies was applied by a piezo.
Redistributions of intensity on the fluorescence spectra were observed and it was
attributed to the repopulation of the domains of different elasticity within the optical
detecting volume. Two stages of behavior under vibration loading were observed. In
the first stage continuous damage carried on until certain limit, by which the second
stage, e.g. breakage, followed in a discontinuous manner.











4Symbols and abbreviations
σ principal stress along the loading axis 1
σ principal stress in radial direction 2
σ principal stress in tangential direction 3
σ total stress (sum of three principal stresses)
R ruby fluorescence emission line at 694.2 nm 1
Rission line at 692.8 nm 2
Δλ wavelength shift
Δλ maximum wavelength shift within the contact area 0
E Young’s modulus
E* effective Young’s modulus
D damage
ν Poisson’s ratio
a radius of the contact circle c
R radius of the ruby sphere
F loa