• Journal of the Korean Wood Science and Technology
• /
• v.27 no.4
• /
• pp.51-56
• /
• 1999

Finite element method was utilized to analyze crack tip stress and displacement field under drying stress case as stepwise loading. Opening mode of single-edge-notched model was employed and analyzed by linear elastic fracture mechanics of plane stress case. The drying stresses were applied as stepwise loads at the boundary elements of the model with 10 steps of time serial. The stress intensity factor($K_I$) for opening mode reached to its maximum just prior to the stress reversal. The $K_I$ from the displacement fields revealed 1.7 times higher than those from stress fields. By comparing the two sets of $K_I$ from displacement and stress fields, single parameter $K_I$ showed its validity to characterize displacement fields around the crack tip front while stress field could not be characterized due to large variations between two sets of data.

• Journal of the Korean Society of Industry Convergence
• /
• v.9 no.1
• /
• pp.37-44
• /
• 2006

Stress and displacement fields of a Mode III crack propagating along the normal to gradient in an orthotropic functionally gradient materials (OFGM), which has (1) an exponential variation of shear modulus and density, and (2) linear variation of shear modulus with a constant density, are derived. The equations of motion in OFGM are developed and solution to the displacement and stress fields for a propagating crack at constant speed though an asymptotic analysis. The first three terms in expansion of stress and displacement are derived to explicitly bring out the influence of nonhomogeneity. When the FGM constant ${\zeta}$ is zero or $r{\rightarrow}0$, the fields for OFGM are almost same as the those for homogeneous orthotropic material. Using the stress components, the effects of nonhomogeneity on stress components are discussed.

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

• Proceedings of the KSME Conference
• /
• 2001.11a
• /
• pp.3-8
• /
• 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
• /
• v.30 no.3 s.246
• /
• pp.249-259
• /
• 2006

Stress and displacement fields of a propagating Mode III crack in an orthotropic functionally gradient material (OFGM), which has (1) linear variation of shear modulus with a constant density, and (2) an exponential variation of shear modulus and density, are derived. The equations of motion in OFGM are developed and solution to the displacement and stress fields fer a propagating crack at constant speed though an asymptotic analysis. The stress terms associated with $\gamma^{-1/2}\;and\;\gamma^{0}$ are not affected by the FGM constant $\zeta$ which is nonhomogeneous parameter, only on the higher order terms, the influences of nonhomogeneity on the stress are explicitly brought out. When the FGM constant $\zeta\;is\;zero\;or\;\gamma{\rightarrow}0$, the fields for OFGM are almost same as the those for homogeneous orthotropic material. Using the stress components, the effects of nonhomogeneity on stress components are discussed.

• Proceedings of the KSME Conference
• /
• 2000.11a
• /
• pp.111-116
• /
• 2000

A semi-infinite interfacial crack propagated with constant velocity in two bonded anisotropic strip under out-of-plane clamped displacements is analyzed. The asymptotic stress and displacement fields near the crack tip are obtained, where the results get more general expressions applicable not only to isotropic/orthotropic materials but also to the extent of the anisotropic material having one plane of elastic symmetry for the interfacial crack. The dynamic stress intensity factor is obtained as a closed form, which is decreased as the velocity of crack propagation increases. The critical velocity where the stress intensity factor comes to zero is obtained, which agrees with the lower value between the critical values of parallel crack merged in the material 1 and 2 adjacent to the interface. The dynamic energy release rate is also obtained as a form related to the stress intensity factor.

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.39 no.2
• /
• pp.143-156
• /
• 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
• /
• v.24 no.2 s.173
• /
• pp.496-505
• /
• 2000

A semi-infinite parallel crack propagated with constant velocity in two bonded anisotropic strip under anti-plane clamped displacement is analyzed. Using Fourier integral transform a Wiener-Hopf equation is derived. By solving this equation the asymptotic stress and displacement fields near the crack tip are determined, where the results give the more general expression applicable to the extent of the anisotropic material having one plane of elastic symmetry for the parallel crack. The dynamic stress intensity factor and energy release rate are also obtained as a closed form, which are the results applicable to the problem both of dynamic and static crack under the same geometry as this study. The stress intensity factor approaches zero at the critical crack velocity which is less than the shear wave velocity, but in typical case of isotropic or orthotropic material agrees with the velocity of shear wave. Also a circular shear stress around crack tip is considered, from which the stress is shown to be approximately symmetric about the horizontal axis. Referring to the maximum stress criteria, it could be shown that a brenched crack is formed by crack growth as crack velocity increases.

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.25 no.6
• /
• pp.949-958
• /
• 2001

A semi-infinite interfacial crack propagated with constant velocity in two bonded anisotropic strips under out-of-plane clamped displacements is analyzed. Using Fourier integral transform the problem is formulated and the Wiener-Hopf equation is derived. By solving this equation the asymptotic stress and displacement fields near the crack tip are obtained, where the results get more general expressions applicable not only to isotropic/orthotropic materials but also to the extent of the anisotropic material having one plane of elastic symmetry for the interfacial crack. The dynamic stress intensity factor is obtained as a closed form, which is decreased as the velocity of crack propagation increases. The critical velocity where the stress intensity factor comes to zero is obtained, which agrees with the lower value between the critical values of parallel crack merged in the material 1 and 2 adjacent to the interface. Using the near tip fields of stresses and displacements, the dynamic energy release rate is also obtained as a form of the stress intensiy factor.

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.36 no.9
• /
• pp.985-996
• /
• 2012

An unsteadily propagating permeable crack in piezoelectric materials (PMs) under anti-plane shear mechanical loading and in-plane electric loading is studied. The equilibrium equations for a transiently propagating crack in a PM are developed, and the solutions on the stress and displacement fields for a permeable crack though an asymptotic analysis are obtained. The influences of piezoelectric constant, dielectric permittivity, time rate of change of the crack tip speed and time rate of change of stress intensity factor on the stress and displacement fields at the transiently propagating crack tip are explicitly clarified. By using the stress and displacements, the characteristics of the stress and displacement at a transiently propagating crack tip in a PM are discussed.