IUST ICI / The 2nd International Conference on Composites:
Characterization, Fabrication and Application (CCFA-2) Dec. 27-30, 2010, Kish Island, Iran
Fatigue-Life Assessment of Micro-sized Silicon Components Subjected to Axial Loads(Times Roman, bolded, Font 12, centered)
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1A. Alexander* and 2M. Farahani(Times Roman, Font 12, centered)
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1Graduate student, 2Professor, Department of Mechanical Engineering,Ryerson University, 350 Victoria Street, Toronto, Ontario M5B 2K3, Canada(Times Roman, Font 10, italic, centered)
*(Tel: (416) 979-5000 Ext. 7707, e-mail: )
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Abstract(Times Roman, Font 12, Bolded)
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A fatigue-damage model for durability assessment of micro-sized silicon components is proposed. The components of this model have been developed based on the physics of crack initiation and damage progress on the most easily damaged planes. This approach may be of great importance in durability assessment of silicon-based MEMS components, while the complexity of laboratory fatigue testing, micro-sized specimen preparation, and the high expenses associated with the fatigue tests of micro-sized silicon components are of great concern. Fatigue-damage accumulation of silicon micro-components is accompanied with the formation of inclined micro-critical planes of {111} on the fracture surface as a means of dissipating energy during fatigue-damage progress, which in principal coincides with the mechanism of fatigue damage accumulation approach. Predicted fatigue lives based on the damage model were found to be in good agreement with experimental fatigue-life data of these components reported in the literature. Correlations are within a factor of ±2.5 for short and long lives, which are within the limits of acceptance. (Up to 200 words, Times Roman,font 10, left & right margins: 1.5 inches)
Keywords:Fatigue-damage analysis; critical planes; silicon micro-components; micro-electro-mechanical systems (MEMS)(Up to 5 words, Times, font 10)
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1. Introduction(First heading, bolded, Times Roman 12)
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Reliability and durability assessment is extremely critical as the structure and feature dimensions are shrunk towards the micro-scale. The smaller the micro-component, the more likely it is to move, aggregate, decompose, or change shape, composition or morphology as the micro-component experiences mechanical-,thermal-, or chemical-loading cycles. Durability assessment of micro-scale devices such as air-bag deployment sensors and blood-pressure sensors, pressure transducers and jet-cartridge nozzles necessitate a high degree of reliability.(Text: Times Roman,font 10, left, right, top and bottom margins 1.25 inches)
Silicon and silicon-based materials are the most commonly used materials in MEMS devices. Silicon-based micro-components are dominant structural materials for micro-machines. The thin films of silicon-based materials are commonly used in actuators, power generation, and other safety-critical and high-performance applications. These microfilms are often subjected to aggressive mechanical and chemical environments. In spite of a decade of investigation on fatigue failure of silicon-based materials, the failure mechanism of micro-scale thin silicon films has not been fully understood. Silicon is a brittle material at room temperature. In the absence of hydrostatic confining pressures to suppress fracture, silicon displays no dislocation activity, even at high stresses [1-2] thus silicon displays no time-dependent cracking when subjected to cyclic-loading conditions. However, experimental results have shown otherwise. Silicon-based thin films degrade and fail under cyclic-loading conditions in ambient air and at room temperature [3,4]. Crack initiation and growth have also been reported [3] in micro-sized silicon films even in the absence of pre-cracks under fatigue loading.
2.Main level heading(Bolded, Times Roman 12)
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2.1 Second level heading(Bolded, Times Roman 10)
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Critical dimensions at which micro-scale structure behavior starts to significantly deviate from bulk-material behavior are not well identified. Therefore, there is always a great need for further experiments to establish mechanical properties of micro-scale components. Properties such as strength, toughness, crack initiation and propagation, stick-slip behavior, and yield characteristics are reported to be different for micro-scale components from those of bulk materials [8].
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2.1.1Third level heading(Bolded, Times Roman 10)
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Uniaxial stressing of silicon at room temperature by Walson and Birnbaum [11] has failed to produce evidence of substantial dislocation motion. Macro-specimens always fail at relatively low stresses, presumably due to the effects of flaws. It has been shown that for silicon materials, plastic flow occurs during indentation [12], because stress under the diamond indenter has a large hydrostatic component and very high shear stresses can be reached locally. Transmission electron microscopy (TEM) studies [13] of indentations produced in silicon under light loads clearly verified that dislocations had been produced as a result of the indentation at room temperature. Silicon has widely been examined for its unique monotonic and cyclic materials response. This material combines the slip system of the FCC structure and the lattice friction that characterizes the BCC materials. The lattice friction can be modulated based on temperature and strain rate [14,15]. (Note: the paragraphs after the first paragraph starts with an intend)
The range of maximum shear stress max and shear strain obtained from the largest stress and strain Mohr’s circles at angles 1 and 2 during a cycle and the corresponding normal stress range n and the normal strain range n on that plane are the components of the critical plane energy-based fatigue-damage parameter. Figure 1 presents the largest stress and strain Mohr’s circles at which the normal and shear stress and strain components yield the highest materials damage on the critical plane.
The proposed model correlates fatigue lives by normalizing the normal- and shear-strain energies by the axial and shear fatigue properties, respectively, and hence the parameter uses no empirical weighting factor:(Note: one space before and after each equation)
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where and are the axial fatigue-strength coefficient and axial fatigue-ductility coefficient, respectively, and and are the shear fatigue-strength coefficient and shear fatigue-ductility coefficient, respectively.
Figure 1 presents the rate of stiffness decay as the number of cycles (Ni) increases. Fatigue strainlife data has also been used to determine the other fatigue coefficients of , ,, and . The fatigue coefficients for silicon micro-components are listed in Table 1.
A critical-plane energy-based fatigue damage parameter has been developed based on the physics of crack initiation and damage progress on the most damaging planes. In silicon micro-components, fatigue-damage accumulation took place as inclined micro-critical planes of {111} were formed and coalesced on the fracture surface as a means of dissipating energy during fatigue-damage progress, which was found to be in agreement with the basis of strain energy damage approach. Based on this damage approach, the shear and normal stress and strain components acting on critical planes are driving forces of the crack causing fatigue-damage accumulation over life cycles. As the number of cycles progressed, fatigue damage was progressively increased and the materials strength was reduced until final failure occurred.
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Figure 1: Stiffness degradation rate of the silicon micro-components as the number of cycles increased [9].
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Table 1: Tensile and fatigue coefficients for silicon micro-sized components.
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E(GPa) / K
(GPa) / n /
(GPa) / G
(GPa) /
(GPa) / b / c
90140 / 72 / 0.50 / 3.105 / 35 / 1.80 / 0.02 / 0.01
Note: (SI units only)
Note: Format of the manuscript (summary)
A manuscript should include a title, name of authors and their addresses. Corresponding author should be indicated by * providing her/his telephone and e-mail address. Provide affiliations of authors.
An abstract of not more than 200 words is required. Key words should not exceed 5 words/phrases. The paper may include introduction, theory/ approach/ experimental procedure, results, discussion, conclusions, acknowledgement and references. Figures and tables are inserted within the text with a proper address to them within a text.The length of manuscript should not exceed 6-pages.
References
[1] Alexander, A. (2000),International Journal of Fatigue22, 295305.
[2] Hill, M.J.,and Rowcliffe, D.J. (2001), Journal of Materials Science9, 15691576.
[3] Brown, M.W. and Miller, K.J. (1982), Two decades of progress in the assessment of multiaxial low cycle fatigue life, in: Low-cycle fatigue and life prediction, (Editors: Amzallag, C., Leis, B., and Rabbe, P.),ASTM STP 770, American Society for Testing and Materials, pp. 482-495.
[4] Brown, M.W. and Miller, K.J. (1989), Biaxial and Multiaxial Fatigue,London: ESIS Publication.
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