Study of Static and Dynamic Properties of Cracked Functionally Graded Materials Using Special Finite Elements

• Author / Creator

  Molavi Nojumi, Mohamad

• Functionally graded materials (FGMs), the new generation of materials in which composition and material properties vary continuously with the change of the coordinate position, provide a good opportunity for combining desired properties of different materials for engineering applications such as: wear resistance or thermal barrier coatings avoiding problems like weak bonding strength or high thermal stresses. One of the main types of FGMs is ceramic/metals. Ceramics are brittle; therefore, there is a high possibility of crack existence during the fabrication process or under in-service loading conditions. Analytical solutions available for crack problems in FGMs are restricted to simple geometries and loading conditions due to the mathematical complexity of the governing equations. Therefore, advanced numerical methods should be applied for general analysis of the crack problems in FGMs. In the scope of this research, the static and dynamic properties of FGMs will be investigated using special finite elements with a focus on fracture mechanics. At first, a general finite element procedure is evaluated for investigating the general elasticity problems for linear elastic isotropic FGMs. An accurate 9-node quadrilateral graded element is investigated in which the influence of the variation of material properties is considered at the element level. The implementation of graded elements prevents potential problems in sudden jumps of material properties in traditional finite elements for modelling FGMs. By employing a finite element-finite difference procedure, the performance of the multiple isoparametric graded elements can be studied in dynamic problems. The main contribution of this research is to develop a new graded singular element with built-in higher order terms based on an asymptotic analysis coupled with the Westergaard stress function approach. Using this novel element at the crack tip surrounded with introduced regular graded elements provides an accurate and efficient model for discussing the role of the material gradient over the crack tip stress field in FGMs. This element is also extended to cover dynamic crack problems by constructing the consistence mass matrix considering the kinetic energy of the singular elements. It eliminates the need to use very fine mesh of regular elements near the crack tip. As a result the efficiency is considerably increased and less computational effort is required at each time step. Furthermore, this element does not require any post processing technique to obtain the stress intensity factors which makes it convenient for studying the influence of the gradient of elastic properties, mass density and loading type on the fracture parameters.

• Subjects / Keywords

  • Functionally graded materials
  • Graded finite elements
  • Fracture mechanics

• Graduation date

  Spring 2018

• Type of Item

  Thesis

• Degree

  Doctor of Philosophy

• DOI

  https://doi.org/10.7939/R3MG7G993

• License

  This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for non-commercial purposes. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.