Sgbem was more accurate for computing the stress

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XFEM in predicting the fatigue crack growth. SGBEM was more accurate for computing the stress intensity factors and the fatigue crack growth rate. Furthermore, it was required coarser meshes and much computational time could be saved. As mentioned in this current framework, XFEM requires the level set method for the crack growth prediction, but SGBEM needed less effort for predicting the fatigue crack propagation. Fatigue Crack in Rubber Material
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P a g e | 9 Rubber structures are significantly resistant to fatigue loadings. To be more specific, natural rubber consisting polymers of the organic compound isoprene plus water have a high strength in fatigue loadings. It is worthwhile to investigate the reinforcement methods for rubber-based structures against the fatigue failure. (Cadwell et al.) Applied the one-dimensional fatigue test to natural rubber and SBR in order to compare their reinforcement process. They pointed out that increasing the mean stress value will lead to the reduction in fatigue life of SBR rubber material under the constant strain amplitude loadings. However, this behavior is different for natural rubber in case the mean stress is greater than the stress amplitude: rise in the mean stress significantly increased the fatigue life. The strain-induced crystallization was a well-known method in reinforcement process. However, the criterion, which proved that the strain induced crystallization increased the fatigue life, was not understood well until (Saintier et al.) presented a strain-induced crystallization process to explain the stress ratio effect on fatigue crack initiation and growth of natural rubber. They claimed that it is required to calculate the maximum degree of crystallization at the crack tip relative to the maximum extension of the specimen in order to obtain the maximum tearing energy when damage is observed. The uniaxial fatigue test was implemented on a diablo-shaped specimen with push–pull testing using a scanning electron microscope. Moreover, they referred a relaxing condition by which natural rubber had the high crack growth resistance. They showed that the fatigue crack starts to grow along the normal direction with respect to the loading direction without any significant deviation, due to the weak
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P a g e | 10 anisotropy in the crack tip region. Conversely, the fatigue crack deviates from the natural crack propagation direction due to the strain-induced crystallization and cumulative processes under the uniaxial and non-relaxing conditions. Hence, they could describe the non-relaxed condition relative to the excellent crack growth resistance by using the concept of crack branch extension during the damage initiation and propagation processes. (Rooj et al.) Investigated the effect of adding organo-montmorillonite (OMt) nanoparticles to the carbon black-filled natural rubber composites by observing the microstructure and fracture mechanical behavior with transmission electron and atomic force microscopies. They precisely represented the experimental procedure
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