Analysis of stresses in notched solids under tension and shear
Date of Issue2017
School of Mechanical and Aerospace Engineering
Fracture mechanics is the study of the propagation of cracks in materials. In the framework of linear elastic fracture mechanics, the stress fields and displacement field at the crack tips of notched solids are of concern. Analysing all the three modes of fracture, it is crucial to identify how the stress fields and displacement field varies. Following that, spotting the maximum stress and displacement along the radial coordinate could be vital as well. This study can also then be used for any linear elastic material (first order). One such example is gels usage for tissue engineering. The motivation of this study is to identify the stress fields and displacement field patterns to observe the points along the radial coordinate of a notch crack. Since the governing equations are highly non-linear and are very difficult to solve analytically or even numerically, a computational software, Wolfram Mathematica, was employed to generate graphs and thus aid in the analysis. This report studies the 3 types of stress fields for Modes I and II respectively. They are namely, 𝜎𝜃, 𝜎𝑟 and 𝜏𝑟𝜃 which are the polar stress components. As for Mode III, the report studies 𝜏𝑟𝑧 and 𝜏𝜃𝑧 which are the shear stresses in the radial and circumferential directions respectively. Also for Mode III, the displacement field, 𝑢𝑧, is analysed. Results from the simulations will be discussed in this report and recommendations for future works will be advised according to the results obtained.
Final Year Project (FYP)
Nanyang Technological University