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Theoretical Analysis of Static and Dynamic Growth of Fractal Cracks

Khezrzadeh, Hamed | 2012

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  1. Type of Document: Ph.D. Dissertation
  2. Language: Farsi
  3. Document No: 42818 (09)
  4. University: Sharif University of Technology
  5. Department: Civil Engineering
  6. Advisor(s): Mofid, Massood; Yavari, Arash
  7. Abstract:
  8. The main need in material related design is the true knowledge about the material properties. Existence of the cracks in the structure of materials is one of the main sources of weakness in the materials. Experimental evidences confirm that the surfaces of the cracks are mainly irregular, but in the existing theories in fracture mechanics all of the results are derived through the assumption of mathematical crack with smooth surfaces or at best with simple geometrical shape. In recent years, after it is being confirmed by experimental results that the fracture surfaces are fractals, several researchers tried to investigate the effect of the roughness of the fracture surfaces in the relations of fracture mechanics. In this dissertation, the effect of considering the roughness of fracture surfaces in mode I fracture is investigated. First, the problem of reaching to limiting roughness is being studied. There are experimental evidences that show that there is a limiting roughness for the roughness of fracture surfaces, but so far there was not a theoretical proof for such a phenomenon. In this dissertation by applying a combination of quantum fracture mechanics and fractal fracture mechanics the first theory for interpretation of reaching to terminal roughness is being presented. Comparison between the presented theory and the experimental results about the limiting roughness shows very good agreement. In the continuation the analytical stress functions which could be served as Green’s functions in different types of fractal cracks problems is being presented. By using such functions the complete (not only asymptotic) fields for stress and displacements could be found in the surrounding of fractal cracks. Also the stress intensity factors could be found by the use of such functions, so various problems in the field of fractal fracture mechanics could be solved by the use of these presented functions. An important issue in the safety of structures is detection of the growth of cracks which can either be harmful or harmless. In this dissertation by introducing the stress functions for fractal cracks, the phenomenon of subcritical growth of crack is being investigated and the related formulas and relation is being derived. The analytical results are in concordance with the experimental results. According to the experiments rougher crack could withstand higher loads. After studying the behavior of fractal cracks in the static and quasi-static cases, their behavior in dynamic case is being investigated. In this research at first the order of singularity of stress for a dynamically propagating fractal crack is derived for the first time. After finding the order of stress singularity for a dynamic fractal crack, the dynamic growth process is being studied. In this research by the use of quantum and fractal fracture mechanics upper limits for the nominal velocity of crack propagation are being presented which are surprisingly have good agreement with numerous experimental results about the terminal velocity of crack propagation in brittle materials.


  9. Keywords:
  10. Fractal Fracture Mechanics ; Quantum Fracture Mechanics ; Fractal Dynamic Fracture ; Fractal Stress Function ; Subcritical Crack Growth

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