Abstract
The investigation of multiple crack interactions in fracture mechanics is important to predict the safety and reliability of structures. This paper introduces a numerical investigation used to calculate the J-integral of the main crack behaviour emanating from a semicircular notch and double semicircular notch and its interaction with another crack which may occur in various positions in (TiB/Ti) FGM plate subjected to tensile mechanical load. Young’s modulus of the functionally graded material plate varies along the specimen width (notch radius direction r-FGM) with exponential-law (E-FGM) function. Further, the Poisson’s ratio is taken as a constant in normal direction. For this purpose the variations of the material properties are applied at the integration points and at the nodes by implementing a subroutine USDFLD in the ABAQUS software. The variation of the J-integral according to the position, the length, and the angle of rotation of cracks is demonstrated. The variation of the J-integral according to the position, the length, and the angle of rotation of cracks are examined; also the effect of different parameters for double notch FGM plate is investigated as well as the effect of band of FGM within the ceramic plate to reduce J-integral. According to the numerical analysis, all parameters above played an important role in determining the J-integral.
Highlights
The formations of cracks are strongly depending on the type of materials, loading, environmental aggression and design condition of mechanical components
The present study consists in investigating the 2D simulation used to calculate the J-integral of the main crack behavior emanating from a semicircular notch and double semicircular notch and its interaction with another crack which may occur in various positions in (TiB/Ti) Functionally graded material (FGM) plate under mode I
The graded finite elements are implemented in the FE software Abaqus 6.9 to verify the USDFLD used subroutine given in Appendix1
Summary
The formations of cracks are strongly depending on the type of materials, loading, environmental aggression and design condition of mechanical components. Ismail et al [3] investigated stress intensity factors of double edge cracks in large groove plate under mode I tension. They used finite element method to determine the stress intensity factor via domain integral method. Shu et al [6] studied the problems of three cracks on both edges of finite width sheet under mode I loading They modeled the multiple cracks using finite element method and due to symmetrical effect only half of model is developed. They found that when there are several cracks co-existed, the flexibility of the plate increased and the stress intensity factors at the crack tips decreased. The graded finite elements are implemented in the FE software Abaqus 6.9 to verify the USDFLD used subroutine given in Appendix
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