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Numerical Simulation of Stress Singularities and Crack Propagation Path in Composite Materials Using X-FEM Method

Akhondzadeh, Shamseddin | 2015

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 49798 (09)
  4. University: Sharif University of Technology
  5. Department: Civil Engineering
  6. Advisor(s): Khoei, Amir Reza
  7. Abstract:
  8. In the present study, in order to investigate the nature of stress singularities in isotropic multimaterial wedges and junctions, determination of the singularity order and analytical asymptotic fields in the vicinity of singular points using the eigen-function expansion method are explained. Next, an efficient approach is proposed to model stress singularities within the X-FEM framework. In this approach, the Airy stress function coefficients are employed in conjunction with the standard singular enrichment functions to obtain modified singular enrichments. Performance and accuracy of the proposed method is shown via computation of the energy norm error and the convergence rates are compared with other methods. Our results indicate that convergence rate of the modified approach is higher than other methods in all cases. It is shown that another advantage of the proposed modified singular enrichments is in determination of stress intensity factors using X-FEM solution which does not require any post processing. Moreover, interaction integral technique, was used to compute SIFs; this technique has been widely used for problems containing a crack in homogeneous material. It has been modified in this work so that it can also be used for determination of SIFs for crack tips terminating at a bimaterial interface. Required expressions has been derived for a crack perpendicular to the interface, oblique crack that has two distinct real singularity orders and oblique cracks with two complex conjugate singularity orders, and their accuracy is confirmed by solving various numerical methods. In the final section, crack penetration angles for a crack which terminates at a bimaterial interface are obtained based on the maximum energy release rate criterion, and corresponding graphs are presented for different material young’s modulus ratios, crack intersection angles and boundary loadings. Moreover, crack propagation path for a crack which lies in the first material is studied, which shows if the Young’s modulus of the second material is considerably higher than that of the first material, crack do not penetrate into the interface and deflects before reaching the interface
  9. Keywords:
  10. Extended Finite Element Method ; Crack Growth ; Singularity ; Stress Intensity Factor ; Composite Materials ; Singular Stresses Field

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