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In this paper, numerical solutions of a hypersingular integral equation for curved cracks in circular regions are presented. The boundary of the circular regions is assumed to be traction free or fixed. The suggested complex potential is composed of two parts, the principle part and the complementary part. The principle part can model the property of a curved crack in an infinite plate. For the case of the traction free boundary, the complementary part can compensate the traction on the circular boundary caused by the principle part. Physically, the proposed idea is similar to the image method in electrostatics. By using the crack opening displacement (COD) as the unknown function and traction as right hand term in the equation, a hypersingular integral equation for the curved crack problems in the circular regions is obtained. The equation is solved by using the curve length coordinate method. In order to prove that the suggested method can be used to solve more complicated cases of the curved cracks, several numerical examples are given.

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A method of continuous-discontinuous cellular automaton for modeling the growth and coalescence of multiple cracks in brittle material is presented. The method uses the level set to track arbitrary discontinuities, and calculation grids are independent of the discontinuities and no remeshing are required with the crack growing. Based on Griffith fracture theory and Mohr-Coulumb criterion, a mixed fracture criterion for multiple cracks growth in brittle material is proposed. The method treats the junction and coalescence of multiple cracks, and junction criterion and coalescence criterion for brittle material are given, too. Besides, in order to overcome the tracking error in the level set approximation for crack junction and coalescence, a dichotomy searching algorithm is proposed. Introduced the above theories into continuous-discontinuous cellular automaton, the present method can be applied to solving multiple crack growth in brittle material, and only cell stiffness is needed and no assembled global stiffness is needed. Some numerical examples are given to shown that the present method is efficient and accurate for crack junction, coalescence and percolation problems.

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We propose a new method for the approximate description of the crack opening displacement caused by the action of two symmetric forces applied to the opposite faces of a crack originating from a concentrator. The solution is sought in the form of a sum of asymptotic and correction terms. The asymptotic term is obtained by applying the operation of inversion to the well-known solution for a half plane with edge crack. The correction term contains unknown coefficients and is negligibly small as compared with the first term if either the point of application of a force or a current point of the crack surface is located near the crack tip. It is shown that the realization of this method reduces to several arithmetic procudures. The high accuracy of the proposed method is demonstrated by analyzing various examples.

Dynamic simulations of the fracture toughness as a function of the orientation and tem- perature were carried out and compared with experimental results obtained by in-situ loading pre-cracked NiAl single crystals inside a scanning force microscope (SFM). In order to compare the simulations with the experiments the problem of the short crack with dislocations was solved for general loading and arbitrary slip line directions. The stress and strain field obtained could be directly connected to FEM calculations which allowed the examination of the stability of micro cracks at notches. The effect of different fracture conditions for biaxial loading were studied in detail.

The dynamic simulation yielded predictions of K1C, slip line length and dislocation distri- butions as a function of loading rate, temperature and orientation. These predictions were tested by in-situ loading NiAl single crystals inside a SFM at various temperatures. The local COD, slip line length and apparent dislocation distribution at the surface were measured as a function of the applied load and the temperature. The experiments clearly demonstrated that dislocations emit from the crack tip before unstable crack jumps occur. The local COD could be directly related to the number of dislocations emitted from the crack tip. With increasing temperature the number of dislocations and the local COD increased before unstable crack jumps or final fracture occurred.

Recent studies have shown that high stress concentrations at moving crack tips in the intermetallic compound NiTi can induce a crystalline-to-amorphous (C-A) transformation of the crack tip region. This stress-induced C-A transformation has a temperature dependence and crystallization behavior similar to those of ion irradiation-induced C-A transformation of NiTi. The present study examines if these similarities between stress- and irradiation-induced amorphization hold true for two other intermetallic compounds, CuTi and Ni3Ti. In situ straining was performed in an intermediate-voltage transmission electron microscope. The presence or absence of an amorphous phase was determined by dark field imaging and selected area diffraction of crack tip regions. Crack tips in both CuTi and Ni3Ti were found to remain crystalline upon fracture. The observed absence of stress-induced amorphization in Ni3Ti is consistent with its known absence during irradiation, but the absence in CuTi differs from its known irradiation-induced amorphization behavior. Reasons for the similarity and difference are discussed.

In this investigation, the fracture and tensile properties of die cast and thixomolded magnesium alloys are compared and shown to be dependent on the microstructure of the test specimens. The principal features of a die cast structure that inhibit crack propagation and contribute to high ductility are the presence of highly structured primary α-magnesium dendrites and a continuous network of the α-magnesium phase. The lower tensile properties of thixomolded magnesium alloys are attributed to the presence of nodular a-magnesium dendrites. Cracks propagate around the nodular dendrites through the divorced eutectic that surrounds the nodular α-magnesium dendrites. In the thixomolded alloys, there is also a less developed continuous network of the α-magnesium phase.

We propose a self-consistent criterion for crack propagation versus dislocation emission, taking into account the effects of crack-tip blunting. Continuum concepts are used to evaluate the evolving competition between crack advance and dislocation nucleation as a function of crack- tip curvature. This framework is used to classify crystals as intrinsically ductile or brittle in terms of the unstable stacking energy, the surface energy, and the peak cohesive stresses achieved during opening and shear of the atomic planes. We find that ductile-brittle criteria based on the assumption that the crack is ideally sharp capture only two of the four possible fracture regimes. One implication of the present analysis is that a crack may initially emit dislocations, only to reinitiate cleavage upon reaching a sufficiently blunted crack-tip geometry.

A continuum model based upon the Peierls-Nabarro description of a dislocation ahead of a crack is used to evaluate the critical mode I loading for dislocation nucleation at the tip of a finite, pre-blunted crack. A similar approach is used to evaluate the critical mode I loading for atomic decohesion. Results are presented for various crack tip root radii (a measure of bluntness), for several crack lengths. It is shown that increasing the crack length increases the critical energy release rate for both material behaviors. Increasing the bluntness of a crack tip always increases the required loading for atomic decohesion but nucleation thresholds are initially decreased by very small increases in crack tip bluntness. Nucleation thresholds are later increased after reaching significant crack tip blunting. Implications for ductile versus brittle competition are discussed by comparing the ongoing competition between these two different material behaviors.

The present work investigates the effects of a passive film formed during stress corrosion cracking on ductile/brittle fracture behavior, considering the interaction of a dislocation with a thin- film-covered crack under an applied remote load. The dislocation emission from the thin-film- covered crack tip is analyzed, on the basis of the two-dimensional Rice-Thomson model, for screw and edge dislocations. The results show that the nominally critical stress intensity factor for dislocation emission is related to the thin film thickness, the properties of the film and the loading conditions. For a given loading mode and a given crack length, there exists a critical value of the film thickness at which the film does not influence the dislocation emission. When the film thickness is smaller than the critical value, a harder thin film makes the dislocation emission easier and a softer film makes the dislocation emission more difficult. The opposite is also true if the film thickness is larger than the critical value.

Mode-III fracture propagation in a two-dimensional continuum model is studied the- oretically. The material is assumed to be isotropic and linearly elastic with a frictional dissipation, and the crack-tip r-gion is modeled by a cohesive zone. As the externally ap- plied load increases, the steady-state crack speed increases to a maximum value which can be substantially smaller than the sound speed when the dissipation is large. The fracture energy also becomes dependent on the velocity. 2ff7e9595c