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Elastic behaviour of an edge dislocation near a sharp crack emanating from a semi-elliptical blunt crack
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The interaction between an edge dislocation and a crack
emanating from a semi-elliptic hole is dealt with. Utilizing the
complex variable method, closed form solutions are derived for
complex potentials and stress fields. The stress intensity factor at
the tip of the crack and the image force acting on the edge
dislocation are also calculated. The influence of the morphology of
the blunt crack and the position of the edge dislocation on the
shielding effect to the crack and the image force is examined in
detail. The results indicate that the shielding or anti-shielding
effect to the stress intensity factor increases acutely when the
dislocation approaches the tip of the crack. The effect of the
morphology of the blunt crack on the stress intensity factor of the
crack and the image force is very significant. 相似文献
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The model of a screw dislocation near a semi-infinite wedge crack tip inside a nano-circular inclusion is proposed to investigate the shielding effect of nano inclusions acting on cracks. Utilizing the complex function method, the closed-form solutions of the stress fields in the matrix and the inclusion region are derived. The stress intensity factor, the image force, as well as the critical loads for dislocation emission are discussed in detail. The results show that the nano inclusion not only enhances the shielding effect exerted by the dislocation, but also provides a shielding effect itself. Moreover, dislocations may be trapped in the nano inclusion even if the matrix is softer than the inclusion. This helps the dislocation shield crack, and reduces the dislocation density within the matrix. 相似文献
5.
We extend here the Bilby-Eshelby approach of 2-D crack representation with dislocation pileups to treat 3-dimensional cracks of general geometry. Cracks of any specified external bounding 3-D contour under general loading conditions are represented by sets of parametric Somigliana loops that satisfy total (interaction, self, and external) force equilibrium. Loop positions are solved by using a time integration scheme till equilibrium is achieved. The local Burgers vector is suitably adjusted to be proportional to the local applied surface traction on the crack. The developed method is computationally advantageous, since accurate crack stress fields are obtained with very few concentric parametric loops that adjust to the external crack shape and the local force conditions. The method is tested against known elasticity solutions for 3-D cracks and found to be convergent with an increase in the number of pileup dislocation loops. The method is applied to the determination of the stress field around a 3-D Griffith crack under general loading and a grain boundary crack before and after branching. 相似文献
6.
《Journal of Physics and Chemistry of Solids》1987,48(11):1007-1014
In this paper, recent developments in the understanding of the dislocation-crack interaction and its relationship to the phenomena of crack tip deformation and fracture toughness are reviewed. An enhanced research activity in this area began with successful observations of the behavior of crack tip dislocations by various techniques, namely etch pits technique, X-ray topography and transmision electron microscopy. The advantages and limitations of these techniques are compared and the information obtained from these experiments are discussed. The results show that dislocations are emitted from a crack tip when the applied stress is sufficiently high. During crack propagation, dislocations are also generated from other bulk sources and the number of these dislocations relative to those from the crack tip may be an important parameter. The elastic theory of the interaction between dislocations and a crack is presented by considering the force on the dislocations. The theory is applied to derive a dislocation emission condition, which may be expressed in terms of a critical stress intensity factor. It is concluded that the dislocations emitted from a crack tip are repelled from the crack tip and this repulsive interaction is responsible for the formation of a dislocation-free zone. These dislocations shield the crack tip from the applied stress and hence contribute to an increase in the fracture toughness. The physical origin of the dislocation-free zone lies in the presence of a barrier to dislocation emission from the crack tip. One of the barriers to dislocation emission is the image stress. With the dislocation-free zone, the crack tip can maintain a finite stress intensity factor following crack tip deformation. The lattice theories of dislocation-crack interaction indicate that the results are consistent with those of the continuum theory. 相似文献
7.
Shielding effect and emission criterion of a screw dislocation near an interfacial blunt crack
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Shielding effect and emission criterion of a screw dislocation near
an interfacial blunt crack are dealt with in this paper. Utilizing
the conformal mapping technique, the closed-form solutions are
derived for complex potentials and stress fields due to a screw
dislocation located near the interfacial blunt crack. The stress
intensity factor on the crack tips and the critical stress intensity
factor for dislocation emission are also calculated. The influence
of the orientation of the dislocation and the morphology of the
blunt crack as well as the material elastic dissimilarity on the
shielding effect and the emission criterion is discussed in detail.
The results show that positive screw dislocations can reduce the
stress intensity factor of the interfacial blunt crack tip
(shielding effect). The shielding effect increases with the increase
of the shear modulus of the lower half-plane, but it decreases with
the increase of the dislocation azimuth angle. The critical loads at
infinity for dislocation emission increases with the increase of
emission angle and curvature radius of blunt crack tip, and the most
probable angle for screw dislocation emission is zero. The present
solutions contain previous results as special cases. 相似文献
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The interaction between a screw dislocation and an interfacial cruciform crack and collinear linear cracks under loads at infinity was investigated. General solutions of complex potentials to this problem were derived by using complex potential theory. As illustrative examples, the closed form solution for a screw dislocation interacting with an interfacial cruciform crack and a linear crack is obtained. The stress intensity factor and critical stress intensity factor for dislocation emission are also calculated. The results show that the shielding effect increases with the increase of the shear modulus and the distance between the two cracks, but it decreases with the increase of dislocation azimuth and the distance between the dislocation and the cruciform crack tip. The critical loads at infinity for dislocation emission increase with the increment of the emission angle, the distance the two cracks and the vertical length of the cruciform crack. 相似文献
10.
Yu. I. Tyalin V. A. Fedorov T. N. Pluzhnikova V. A. Kuranova 《Physics of the Solid State》2000,42(7):1290-1293
Computer simulation technique is used for studying the plastic flow at the tip of an arrested crack in lithium fluoride crystals. Two stages of the dislocation structure formation at the tip of a crack are analyzed: the formation of slip lines at the instant of crack arresting, and their evolution after sample unloading and partial healing of the crack. The size and the number of dislocations in a slip line are determined as functions of the loading force at the instant of crack arresting and on frictional stresses. It is shown that, during sample unloading and healing, some dislocations emerge at the plane of the crack under the action of mutual repulsion and image forces, so that the dislocation density attains its maximum value at a distance from the crack tip. A finite region free of dislocations exists in the immediate vicinity of the crack tip. 相似文献
11.
Abstract Propagation of 3-D fatigue cracks is analyzed using a discrete dislocation representation of the crack opening displacement. Three dimensional cracks are represented with Volterra dislocation loops in equilibrium with the applied external load. The stress intensity factor (SIF) is calculated using the Peach–Koehler (PK) force acting on the crack tip dislocation loop. Loading mode decomposition of the SIF is achieved by selection of Burgers vector components to correspond to each fracture mode in the PK force calculations. The interaction between 3-D cracks and free surfaces is taken into account through application of the superposition principle. A boundary integral solution of an elasticity problem in a finite domain is superposed onto the elastic field solution of the discrete dislocation method in an infinite medium. The numerical accuracy of the SIF is ascertained by comparison with known analytical solution of a 3-D crack problem in pure mode I, and for mixed-mode loading. Finally, fatigue crack growth simulations are performed with the Paris law, showing that 3-D cracks do not propagate in a self-similar shape, but they re-configure as a result of their interaction with external boundaries. A specific numerical example of fatigue crack growth is presented to demonstrate the utility of the developed method for studies of 3-D crack growth during fatigue. 相似文献
12.
Fu-bin Li 《Applied Physics A: Materials Science & Processing》1990,51(4):327-331
This paper evaluates a compact formula incorporating both the Bilby-Cottrell-Swinden (BCS) and the Taira-Tanaka-Nakai (TTN) by considering a rectilinear crack traversing an arbitrary number of zones with different friction stresses. Symmetry is not required. The expressions for the dislocation density and the plastic displacement as well as the stress distribution in the plane of the crack are obtained. 相似文献
13.
V. V. Malashenko 《Technical Physics》2011,56(9):1287-1290
The effect of a high hydrostatic pressure on the dislocation dipole vibration frequency and the forces of dynamic drag of
dislocations by dislocation dipoles and of dislocation pairs by pinned dislocations is studied. Analytical expressions are
obtained for the force of dynamic drag of mobile dislocation pairs by pinned dislocations and for the force of drag of isolated
dislocations by dislocation dipoles in hydrostatically compressed crystals. Hydrostatic compression leads to a significant
increase in these forces. This effect is most pronounced in alkali-halide crystals, where the drag force increases by a factor
of 1.5–2.0. 相似文献
14.
H. Hora 《Applied Physics A: Materials Science & Processing》1983,30(4):217-221
The plane elasticity problem of the interaction between an edge dislocation and an elliptical inhomogeneity is solved, and the image glide-force on dislocation is computed. Contour plots of the force exterted by either an elliptic hole (crack) or a rigid elliptical inhomogeneity show that force is stronger for more elongated shapes, and that in some cases dislocation trapping effects undergo drastic changes even for slight shape variations. The general case is investigated by means of angular plots of force. They show increasing oscillatory angular depence on increasing both elongation and shear moduli difference. 相似文献
15.
On the interaction between dislocations and cracks in one-dimensional hexagonal quasi-crystals 总被引:1,自引:0,他引:1
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The solution of elasticity problems involving the interaction between dislocations and cracks plays a fundamental role in many practical and theoretical applications. Although elasticity problems involving dislocation or cracks in quasi-crystals have been investigated in many papers, the analysis is limited to a single defect. This paper investigates the interaction of defects in one-dimensional hexagonal quasi-crystals using the complex variable function method. The interaction force between two parallel dislocations is presented and the analytic solutions of elastic fields of interaction between a dislocation and a crack are obtained. A version of the well-known Peach-Koehler formula in one-dimensional hexagonal quasi-crystals is given. 相似文献
16.
The effect of shock-wave loading with an amplitude of 4 GPa and a duration of 10 μs on the localization of plastic flow and
the dynamic fracture of VT-1 cast titanium alloy containing a disk-shaped crack is considered. It is found that the crack
size decreases in the direction of shock wave propagation, the dislocation density grows and adiabatic shear bands appear
near the crack, and secondary cracks originate in the areas of localized flow near the crack edges. The strain, strain rate,
dislocation density, rate of dislocation generation, and dislocation velocity near and away from the healing crack are estimated. 相似文献
17.
根据本征方程,研究磁电弹性体中若干平行螺型位错与Griffith裂纹的相互作用.结合Muskhelishvili方法和算子理论,得到磁电弹性体中由位错和裂纹所诱导的应力场、电场和磁场的解析解.数值算例表明:在裂纹的端点及位错点上仍然存在应力的奇异性,离位错点越远处广义力越小,结论与已有的结果相符,证明了结论的正确性.当位错点与裂纹端点距离越近时,裂纹与位错间的应力场越小,并逐渐趋近于零. 相似文献
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Screw dislocations interacting with two asymmetrical interfacial cracks emanating from an elliptical hole
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The interaction between screw dislocations and two asymmetrical interfacial cracks emanating from an elliptic hole under loads at infinity is studied. The closed-form solution is derived for complex potentials. The stress intensity factor and the critical applied stress for the dislocation emission are also calculated. In the limiting cases, well-known results can be obtained from the present solutions. Moreover, new exact solutions for a screw dislocation interacting with some complicated cracks are derived. The results show that the shielding effect increases with the increase in the length of the other cracks and the minor semi axis, but decreases with the increase of dislocation azimuth. The repulsion acting on the dislocation from the other phase and the other crack extend in the horizontal direction, which makes the dislocation emission at the crack tip take place more easily, but the minor semi axis of the elliptical hole extending in the vertical direction makes it more difficult. 相似文献
20.
Analyses are reviewed where plastic flow in the vicinity of an interfacial crack is represented in terms of the nucleation and glide of discrete dislocations. Attention is confined to cracks along a metal-ceramic interface, with the ceramic idealized as being rigid. Both monotonic and fatigue loading are considered. The main focus is on the stress and deformation fields near the crack tip predicted by discrete dislocation plasticity, in comparison with those obtained from conventional continuum plasticity theory. The role that discrete dislocation plasticity can play in interpreting interface fracture properties in the presence of plastic flow is discussed. 相似文献