• Transactions of the Korean Society of Mechanical Engineers A
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• v.39 no.2
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• pp.143-156
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• 2015

The stress and displacement fields at the crack tip were studied during the unsteady propagation of a mode III crack in a direction that was different from the property graduation direction in functionally graded materials (FGMs). The property graduation in FGMs was assumed based on the linearly varying shear modulus under a constant density and the exponentially varying shear modulus and density. To obtain the solution of the harmonic function, the general partial differential equation of the dynamic equilibrium equation was transformed into a Laplace equation. Based on the Laplace equation, the stress and displacement fields, which depended on the time rates of change in the crack tip speed and stress intensity factor, were obtained through an asymptotic analysis. Using the stress and displacement fields, the effects of the angled property variation on the stresses, displacements, and stress intensity factors are discussed.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.26 no.9
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• pp.1753-1763
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• 2002

Stress and displacement fields for a propagating crack in a functionally gradient material (FGM) which has shear modulus as $\mu$=$\mu$$\_$0/(1＋ζX) are derived. The equations of motion in FGM which is nonhomogeneous material are different from those of homogeneous material. The stress intensity factors in stress fields have influence on odd terms of γ$\^$n/2-1/(n=1,3,5,...,) but stress at crack tip only retains term of γ$\^$-1/2/, where the γ is a radius of cylindrical coordinates centered at crack tip. When the FGM constant ζ is zero or γ→0, the fields for FGM are almost same as the those for isotropic material.

• Proceedings of the KSME Conference
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• 2001.11a
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• pp.3-8
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• 2001

Dynamic stress intensity factors (DSIFs) are obtained when a crack propagates with constant velocity in rectangular functionally gradient materials (FGMs) under dynamic mode III load. To obtain the dynamic stress intensity factors, it is used the general stress and displacement fields of FGMs for propagating crack and the boundary collocation method (BCM). The stress intensity factors and energy release rates are the greatest in the increasing properties $(\xi>0)$, next constant properties $(\x=0)$ and decreasing properties $(\xi<0)$ under constant crack tip properties and crack tip speed.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.28 no.10
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• pp.1500-1508
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• 2004

Stress and displacement fields for a crack propagating along interface between isotropic material and functionally gradient one with linear property gradation along X direction are developed. The stress and displacement fields are obtained from the complex function of steady plane motion for isotropic and functionally gradient material (FGM). The stresses and displacement in isotropic material of bimaterial are not influenced by nonhomogeneity, however, the fields in FCM are influenced by nonhomogeneity in the terms of higher order, n$\geq$3. When the nonhomogeneous parameter in FGM is zero, or in area close to crack tip, the fields are identical to those of isotropic-isotropic bimaterial. Using these stress components, the effects of nonhomogeneity on stresses are discussed.

• Composites Research
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• v.26 no.6
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• pp.363-372
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• 2013

Numerical simulation for Resin Transfer Molding manufacturing process is attempted by using the eXtended Finite Element Method (XFEM) combined with the level set method. XFEM allows to obtaining a good numerical precision of the pressure near the resin flow front, where its gradient is discontinuous. The enriched shape functions of XFEM are derived by using the level set values so as to correctly describe the interpolation with the resin flow front. In addition, the level set method is used to transport the resin flow front at each time step during the mold filling. The level set values are calculated by an implicit characteristic Galerkin FEM. The multi-frontal solver of IPSAP is adopted to solve the system. This work is validated by comparing the obtained results with analytic solutions. Moreover, a localization method of XFEM and level set method is proposed to increase the computing efficiency. The computation domain is reduced to the small region near the resin flow front. Therefore, the total computing time is strongly reduced by it. The efficiency test is made with a simple channel flow model. Several application examples are analyzed to demonstrate ability of this method.