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- Type of Document: Ph.D. Dissertation
- Language: Farsi
- Document No: 40224 (08)
- University: Sharif University of Technology
- Department: Mechanical Engineering
- Advisor(s): Farrahi, Gholamhossein; Smith, D. J
- Abstract:
- Residual stresses are defined as the stresses supported in a body in a fixed reference configuration where there is the absence of external forces and thermal gradients. Knowledge of the distribution and magnitude of the residual stresses is consequently important in determining the component fatigue life. While modeling of the manufacturing process is often very difficult, it is also well known that it can be difficult to measure complete patterns of residual stresses throughout the engineering component, due to limitations of facility access, measurement time or specimen dimensions, and only limited measurements are made. Most often, the problem are addressed in the inverse sense, incomplete set of residual stresses measurements are experimentally known while the unknown complete distribution of residual stress state needs to be found. Here, an analytical method for reconstructing residual stresses within axisymmetric plane problems (including shot peening, turning and autofrettage process) and Cartesian plane problems (including beam bending, welding and general solution) is presented. In this research, based on the concept of the Airy stress function, an inverse approach would be presented to reconstruct the residual stress field from limited incomplete measurements. In contrast to previous research, no numerical model based on assumed eigenstrain distribution would be utilized and the entire domain of residual stress field would be determined using a limited set of data by solving the stress equilibrium equations directly. A new general solution based on the approximated stress function would be proposed together with satisfying all of the requirements of continuum mechanics. To ensure that the method would satisfy the whole requirements of continuum mechanics, the equilibrium equations and the traction free boundary conditions would be satisfied while vanishing of the mean residual stress on the entire domain would be imposed. As well as there exist the flexibility to impose the type of the physical behavior of residual stresses to attain the meaningful stress field. The other advantage of this approach lies in its flexibility, where different sets of measurements and information about different components of the stress state can be incorporated. Also the efficiency of the method has been demonstrated by achieving an excellent agreement between the model prediction and experimental measured stresses in the sense of least square approximation in various processes without the necessity of using iterative solution. Finally the solution of the inverse problem has been regularized using Tikhonov- Morozov stabilization theory.
- Keywords:
- Residual Stress ; Shot Peening ; Turning ; Autofrettage Process ; Inverse Problem ; Limited Measurement ; Stabilization Theory ;
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