«by the Low Velocity Impact of Spherical Particles by Amirhossein Mohajerani A thesis submitted in conformity with the requirements for the degree of ...»
Chipping and Wear of Glass Edges by the Low Velocity Impact of
A thesis submitted in conformity with the requirements
for the degree of Doctor of Philosophy
Graduate Department of Mechanical and Industrial Engineering
University of Toronto
© Copyright by Amirhossein Mohajerani (2011)
Chipping and Wear of Glass Edges by the Low Velocity Impact of
Department of Mechanical and Industrial Engineering University of Toronto Abstract The edge rounding of brittle materials by vibratory finishing, VF, was investigated. Borosilicate glass and silicon nitride specimens were processed in two typical VF setups. In all cases, the processed specimens exhibited wear and chipping at their edges, whereas their flat surfaces remained intact. Edge chipping was strongly affected by the edge geometry and process parameters such as the media size and vibration amplitude of the finisher. Therefore, to achieve smooth chip-less edge, samples were processed in several steps, starting with the least energetic conditions, followed by more energetic ones as the edge became progressively blunter. The analysis of edge wear by VF revealed a new mechanism of wear, not previously reported in the literature. A stochastic numerical model was subsequently developed to model this mechanism of wear. To confirm the validity of the model, the model predictions were compared to the experimental observations of wear in the vibratory finisher. The model was used to investigate the effect of various VF process parameters on the edge wear of brittle materials.
A VF simulator was used to investigate wear and chipping under more controlled conditions.
The VF simulator launched particles against the specimens at adjustable velocities and impact angles. The effect of particles’ shape, and impact velocity and angle, on the wear of glass edges was investigated. Fundamental differences were observed between wear by abrasive and smooth particles. These differences were attributed to the mechanisms of material removal by abrasive ii and smooth balls. Abrasive balls remove material by the sharp indentation of their surface asperities, whereas smooth particles lack such sharp peaks and hence apply blunt indentation on the edges. To identify the fundamental differences between material removal by sharp and blunt indenters, a series of indentation experiments were carried out on glass edges. Subsequently, these differences werediscussed in terms of their implications on wear by abrasive and smooth particles.
iv Acknowledgements First and foremost, I would like to express my sincere gratitude and appreciation to my supervisor, Professor Jan K. Spelt, for providing the opportunity to pursue a doctoral dissertation and for graciously offering his expertise and support in pursuit of my research and career objectives. I also thank Professor Zhirui Wang and Professor Adreas Mandelis for their time and contributions as doctoral dissertation committee members.
I would like to express my gratitude to the Natural Sciences and Engineering Research Council of Canada. This research would not have been possible without their financial support.
I extend my thanks to Mayank Singh and Shivinder Babbar for doing exceptional and excellent jobs as research assistants. Thanks are also due to my lab mates, Aboutaleb Ameli, Siva Nadimpalli, Naresh Datla, Shahrokh Azari, Greg Jhin, and Dwayne Shirley, for sharing and discussing all kinds of ideas and for being always there whenever I needed help from them in anything.
I would like to send special thanks to my angel, Anna, for all the love and happiness she brought to my life.
vTable of Contents
Table of Contents
List of Figures
Background and motivation
1.2 Literature Review
1.3 Vibratory finishing
1.3.1 Edge Chipping in Brittle Materials
1.3.2 Wear of Brittle Materials
1.3.3 Overview of the thesis
1.5 Edge rounding of brittle materials by low velocity erosive wear
2.2 Vibratory finishers
2.2.3 Edge chipping
2.3 Edge wear
2.4 The mechanism of edge wear
2.4.1 Rate of edge wear
2.4.2 Geometric characterization of edge roughness
2.6 Numerical modeling of the edge rounding of brittle materials by vibratory finishing
3.2 vi Numerical model
3.3 Indentation force magnitude
3.3.1 Location of media impact
3.3.2 Chip formation
3.3.3 Time scaling
3.3.4 Determination of γ and γ’
3.3.5 Discussion and results
3.4 Edge wear for glass
3.4.1 Role of indentation forces and chip size
3.4.2 Wear progressiveness
3.4.3 MACOR® specimens
3.4.4 Practical implications
3.6 Edge chipping of borosilicate glass by blunt indentation
4.1 Hertzian contact near an edge
4.3 4.3.1 Crack initiation and early stage propagation
4.3.1 4.3.2 Later stage crack propagation
4.3.2 4.3.3 Catastrophic failure
4.3.3 4.3.4 Effect of indenter constraint
4.3.5 Negative indentation distances
4.3.4 4.3.6 Summary of chipping observations
4.3.7 Chipping forces
4.3.8 Comparison of sharp and blunt indentation of edges
4.5 Edge chipping of borosilicate glass by low velocity impact of spherical indenters
5.1 Sharp indenters
5.1.1 vii Impact loading
5.1.2 Edge chipping by quasi-static loading of blunt indenters
5.3 Impact force measurement
5.3.1 Edge chipping under impact
5.3.2 Impact vs. quasi-static chipping forces
5.3.3 Effect of loading rate
5.3.4 Effect of unloading
5.3.5 Effect of lateral constraint
5.5 Erosive wear of borosilicate glass edges by unidirectional low velocity impact of steel balls........ 137 Introduction
6.1 Edge chipping by single indentation
6.3 Globally Unidirectional Impact tests
6.3.1 Effect of edge geometry on chipping
6.3.2 Cyclic crack growth in edge chipping
6.3.3 Comparison with quasi-static indentation
6.3.4 Unidirectional vs. multidirectional impacts
6.5 Erosive wear of borosilicate glass by low velocity unidirectional impact of abrasive spheres........ 164 Introduction
7.2 Numerical model
7.3 Chip formation
7.3.1 Indentation location and force
7.3.2 Time scaling
7.3.3 Determination of γ and γ’
7.3.4 viii Results and discussion
7.4 Experimental results
7.4.1 Determination of γ and γ’ and resulting model predictions
7.4.2 Variation in the force parameter vs. variation in the indentation location
7.4.3 Unidirectional vs. multidirectional impacts
Summary of conclusions
8.1 Future work
ixList of Tables
Table 2-1 The values of A and L approximated by fitting power functions to the experimental edge wear data obtained from glass samples in the bowl and tub finishers. The numbers in the brackets indicate the 95% confidence bounds.
Table 2-2 The values of A and L approximated by fitting power functions to the experimental data obtained from processing silicon nitride samples in the bowl, using abrasive ceramic media of average diameter 7.1 mm. The numbers in the brackets indicate 95% confidence bounds
Table 3-1 Mechanical properties of the test materials
Table 3-2 Coefficient of determination, R2, of the experimental data and the model predictions of the amounts of wear, relative to their respective best-fit average curves (Figs. 11-13).
Table 3-3 The root mean squared roughness, Rq, of 120o edges, averaged from 4 runs of the model..... 63 Table 5-1 Properties of the steel and ceramic balls.
Table 6-1 Critical chamfer width as a function of impact velocity and edge included angle, α. 4 measurements of critical chamfer width for each velocity and edge angle.
x List of Figures
Figure 1-1 Schematic of tub vibratory finisher showing bulk flow direction and workpiece motion (reproduced from ref. ).
Figure 1-2 Schematic diagram of bowl-type vibratory finisher (reproduced from ref. ).
Figure 2-1 Schematic diagram of bowl-type vibratory finisher (reproduced from ref. ).
Figure 2-2 Cross-section of the vibratory tub finisher (reproduced from ref. ) showing direction of media circulation and resulting slope of the free surface. Dimensions in mm
Figure 2-3 Schematic view of a glass sample prepared for processing in the vibratory tub. Two thin strips are attached to the wide sides of the sample to create enough irregularity to its geometry................... 17 Figure 2-4 A glass edge (a) before processing, and (b) after processing in the vibratory tub for one hour, using abrasive ceramic media with average diameter of 11 mm.
Figure 2-5 (a) A chamfered glass edge after being processed in the vibratory tub finisher with steel media, (b) Schematic illustration of the edge, with dashed line demonstrating the initial geometry of the chipped edges (the arrow shows the direction in which the chamfer width narrows), and (c) Schematic illustration of the chamfer cross-section.
Figure 2-6 Typical cross-section of a glass specimen edge after being processed in stages in the vibratory bowl using abrasive ceramic media. Three sizes of media and three amplitudes were applied in 9 steps, each lasting 1 h.
Figure 2-7 Wear band along edges without chipping. Left: silicon nitride edge, angle = 90°. Right: Glass chamfered edge, angle = 120°. Dashed lines indicate the approximate boundaries of the wear band.. 21 Figure 2-8 Flat surface of a glass specimen: (a) after 1 h, and (b) after 3 h processing in the vibratory bowl, using abrasive ceramic media (7.1 mm diameter). The long scratches appeared rarely and were widely spaced.
Figure 2-9 The variation of average roughness, Ra, on the flat surfaces and across the rounded edge as a function of the process duration for a glass sample in the vibratory tub (7.1 mm abrasive ceramic media). Multiple values of roughness are shown at each time corresponding to measurements at 4 random locations on the flat surfaces and 4 locations along the edges.
Figure 2-10 Scanning electron micrograph of typical a) glass and b) silicon nitride edges processed in the vibratory bowl using the spherical abrasive ceramic media (7.1 mm diameter).
Figure 2-11 Schematic of a chamfered glass specimen fixed in the tub finisher to provide a leading and trailing edge relative to the media bulk flow.
Figure 2-12 Schematic of a chamfered glass specimen positioned such that only one side of the edge was exposed to the media, creating an uninterrupted flow of media against the edge of interest................ 26 Figure 2-13 Profile of a glass edge with included angle of 120° processed in the tub for 30 min., and the corresponding values of A and L.
Figure 2-14 Rate of edge wear, REW, as a function of process duration for glass samples processed in (a) the tub, and (b) the bowl finishers. Legends show the included angles of the edges using abrasive ceramic media of average diameter 7.1 mm.
Figure 2-15 The rate of edge wear as a function of processing time for silicon nitride specimens processed in the bowl using ceramic media of average diameter 11 mm.
xi Figure 2-16 Roughness parameter r of glass specimen edges processed in the tub vs. process duration.
The partitioning length was 0.03 mm. Legend shows the edge angle.
Figure 2-17 Roughness parameter r of glass specimens processed in the bowl vs. process duration. The partitioning length was 0.02 mm. Legend shows the edge angle.