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The Analysis of Cracked Atomic Force Microscope Micro-Cantilever by Strain Gradient Theory

Ganji, Hamid | 2017

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 49494 (08)
  4. University: Sharif University of Technology
  5. Department: Mechanical Engineering
  6. Advisor(s): Asghari, Mohsen
  7. Abstract:
  8. The present study deals with the analysis of Atomic Microscope with crack by making use of Strain Gradient Elasticity theory. Empirical observations represent that in micro dimensions, materials show behaviors, which the classic continuum mechanics theories are not able to explain. Thus, taking advantage of non-classic theories, which are capable of explaining such phenomena or behaviors in analyzing materials in micro dimensions seems necessary and of much significance. In this direction, by applying an Euler-Bernoulli beam assumption and neglecting the shear effects, governing equations and boundary conditions of the problem were obtained via taking advantage of variations in Hamilton principle and then were made dimensionless. Then, analytical solution for deflection of a cracked beam was obtained by making use of each of the classic, couple stress and strain gradient theories. In the end, for a specific example of cracked microscope, the solved numerical results obtained from the strain gradient theory as well as the diagrams of dimensionless deflection were presented and compared to those resulted from the classic and couple stress theories. In the resulted diagrams, it can be observed that the solutions obtained from the classic and non-classic theories are much more different in smaller sizes and as the size of the material increases, the amount of difference between these two solutions becomes smaller. In these diagrams, the effects of the number of the cracks, the position of the cracks and the size were analyzed. It can be seen that the less the number of the cracks and their distance from the cantilever tip of the beam are, the greater the deflection of the beam will be. It can be also claimed that as the dimensions become smaller, the discrepancy between the results from the classic and non-classic theories increases, which represents the significance of size effects in micro dimensions
  9. Keywords:
  10. Strain Gradient Theory ; Crack ; Size Effect ; Atomic Force Microscopy (AFM) ; Euler-Bernoulli Beam ; Micro-Scales

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