The interaction between a dislocation and a crack: Closure considerations (original) (raw)
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Interaction between edge dislocations around the tip of a crack
Mechanics of Materials, 1996
The interaction between edge dislocations around the tip of a crack has been analyzed analytically and numerically. It is found that when these dislocations are placed on a cylinder around the crack tip with their slip planes all passing through the tip, the slip force exerted on a dislocation by another dislocation and its images is zero regardless of their locations on the cylinder. Inside as well as outside this cylinder other zero-slip-force positions also exist. The results show that a plastic zone around a crack tip is stable.
1998
A comparison of elastic interaction of a dislocation and a crack for four bonding conditions of the crack plane was made. Four cases of single crystalline material, sliding grain boundary, perfectly bonded interface, and sliding interface were considered. The stress intensity factors arising from edge and screw dislocations and their image forces for the above four cases were compared. The stress intensity factor at a crack tip along the perfectly bonded interface arising from screw dislocation can be obtained from that in a single crystalline material if the shear modulus in the single crystalline material is replaced by the harmonic mean of both shear moduli in the bimaterial. The stress intensity factor at a crack tip along the sliding interface arising from edge dislocation in the bimaterial can be obtained from that along the sliding grain boundary in the single material if the µ/(1 − ν) in the single material is substituted by the harmonic mean of µ/(1 − ν) in the bimaterial where µ and ν are the shear modulus and Poisson's ratio, respectively. The solutions of screw dislocation near a crack along the sliding grain boundary and sliding interface are the same as that of screw dislocation and its mirror image. Generally, the effect of edge dislocation for perfectly bonded interface on the crack propagation is more pronounced than that for the sliding interface. The effect of edge dislocation on the crack propagation is mixed mode for the cases of perfectly bonded interface and single crystalline material, but mode I fracture for the cases of sliding interface and sliding grain boundary. All curves of F x versus distance r from the dislocation at interface to the right-hand crack tip are similar to one another regardless of dislocation source for both sliding interface and perfectly bonded interface. The level of F x for m = 0 is larger than that for m = −1.
The interaction between a dislocation and a crack
International Journal of Fracture Mechanics, 1966
The solution is given in closed form to the problem of the elastic field round a ~ dislocation an d a,. crack in any relative position when the field is independent of one of the three cartesian co-ordinates. The analysis holds for the most general anisotropy.
Comparison of the effects of dislocations around internal and surface cracks on fracture
Materials Science and Engineering, 1987
By comparing the results of internal cracks obtained by Louat with those on surface cracks obtained by Juang and Lee, we find that the physical variables of an internal crack of length 21 are equivalent to the counterparts of a surface crack of length I. If the dislocation is not very close to the free surface, the magnitude of each physical variable of the surface crack is between those of counterparts of the internal crack with the number m of dislocations inside the crack equalling-1 and O. For short cracks, each physical variable is proportional to m. As a result, an internal microcrack appears in the region containing the dislocation. In contrast, for long cracks, we compared the first-order terms for both cracks, and the zero-order terms were found to be the same as those of a semi-infinite crack. Finally, the validity of the actionreaction law is proved for both types of crack.
The dislocation approximation for calculating crack interaction
A simplified method for calculating crack interaction suitable for multicrack arrangements is introduced. It is based on approximating the crackgenerated stress field by that produced by a pair of edge dislocations of opposite signs with Burgers vector equal to the average relative displacement of the crack faces under given load. 1. Introduction. The solution to the problem of interaction of many cracks requires solving systems of integral equations which are, in numerical solutions, reduced to large systems of linear equations (eg. Savruk, 1981). There are approximate methods that simplify this problem and produce smaller systems of algebraic_equations: the dipole asymptotics method (eg. Dyskin and Muhlhaus, 1995) which is valid at distances large compared to the crack dimension; and the approximate method proposed by Kachanov (1987) which yields more accurate results, but has a more complicated algorithm. An alternative approach could be in modelling the crack by a pair of edge dislocations. This method was discussed by Salganik and Mokhel (1990) in application to modelling underground excavations in the case when the Burgers vector was specified. In the method proposed ,here, the Burgers vectors are determined by the crack interaction being equal to the average relative displacement of the crack faces caused by the externally applied load and the stresses created by other cracks in the intact material on the place of the crack in question. The cases of a pair of parallel cracks, a periodical array of equally oriented cracks and two rows of periodical arrays of parallel cracks are considered under plain strain condition (Fig. la, b). Results are compared with known full and numerical solutions. 2. The dislocation approximation for a single crack. For the case of a crack of length 2/ uniformly loaded by normal cro. and shear-r 0 tractions the Burgers vector is b=-A/21, where A is the complex cracK opening area, A=i(-cr 0 +i-r 0)fn(1-v)/G; v is Poisson's ratio and G is the shear modulus (Dyskin and Muhlhaus, 1995). By considering two edge dislocations with Burgers vectors b and-b situated at points-1 and I corresponding to the tips of the approximated crack and using the principle of superposition the complex potentials for the dislocation model of the crack can be obtained cD(z)=z~~oZZ' 't'(z)=-z•¢'(z)+~~=~ (1) Here P 0 =-l 2 (cr 0-i-r 0)14. The crack-generated stresses can then be calculated using Kolosov's formulae (eg. Muskhelishvili, 1953).
An edge dislocation of constant velocity near a static internal crack
International Journal of Fracture, 1995
An edge dislocation of constant velocity near a static internal crack was investigated. The dislocation slip and climb and dislocation source were considered. The crack surface was simulated with static continuous dislocations. After obtaining the distribution of static dislocations in the crack, we calculated the stress field in the entire space. Using the stress distribution, we then computed the stress intensity factors at both crack tips and the image force on the edge dislocation. Numerical results are provided to describe in detail the effect of velocity and crack length on toughness and image force.
Mechanisms of dislocation multiplication at crack tips
Acta Materialia, 2013
Whether a stressed material fractures by brittle cleavage or ductile rupture is determined by its ability to convert elastic strain energy to plastic deformation through the generation and motion of dislocations. Although it is known that pre-existing dislocations play a crucial role in crack tip plasticity, the involved mechanisms are unclear. Here it is demonstrated by atomistic simulations that individual pre-existing dislocations may lead to the generation of large numbers of dislocations at the crack tip. The newly generated dislocations are usually of di↵erent types. The processes involved are fundamentally di↵erent for stationary cracks and propagating cracks. Whereas local crack front reorientation plays an important role in propagating cracks, the multiplication mechanism at stationary cracks is connected with cross-slip in the highly inhomogeneous stress field of the crack. Analysis of the forces acting on the dislocations allows to ⇤ Corresponding author.
Acta Mechanica Solida Sinica, 2007
The effects of dislocation configuration, crack blunting and free surfaces on the triggering load of dislocation sources in the vicinity of a crack or a wedge tip subjected to a tensile load in the far field are investigated. An appropriate triggering criterion for dislocation sources is proposed by considering the configurational forces acting on each dislocation. The triggering behaviors of dislocation sources near the tips of a crack and a wedge are compared. It is also found that the blunting of crack tip and the presence of free surfaces near the crack or the wedge have considerable influences on the triggering load of dislocation sources. This study might be of significance to gaining a deeper understanding of the brittle-to-ductile transition of materials.
Edge dislocations near a cracked sliding interface
1998
The edge dislocations near a cracked sliding interface were investigated. A continuous distribution of edge dislocations with Burgers vector along the y direction was used to simulate a crack of finite length along the sliding interface. From the dislocation distribution the stress field in the entire space was obtained. The stress intensity factors at both crack tips and image force on the edge dislocation were derived. The effects of the dislocation source and shear modulus ratio on both stress intensity factors and image force were also studied. Only mode I stress intensity factors at both tips were found in the composite materials with a sliding interface. The edge dislocations with Burgers vector along the y direction emitted from the crack always shield it to prevent propagation. The above results may reduce to an edge dislocation near a semi-infinite crack along a sliding interface including a sliding grain boundary.
Dislocation nucleation from a crack tip: An analysis based on the Peierls concept
Journal of the Mechanics and Physics of Solids, 1992
DISLOCATION nucleation from a stressed crack tip is analyzed based on the Peierls concept. A periodic relation between shear stress and atomic shear displacement is assumed to hold along the most highly stressed slip plane emanating from a crack tip. This allows some small slip displacement to occur near the tip in response to small applied loading and, with increase in loading, the incipient dislocation configuration becomes unstable and leads to a fully formed dislocation which is driven away from the crack. An exact solution for the loading at that nucleation instability is developed via the J-integral for the case when the crack and slip planes coincide, and an approximate solution is given when they do not. Solutions are also given for emission of dissociated dislocations, especially partial dislocation pairs in fcc crystals. The leveJ of applied stress intensity factors required for dislocation nucleation is shown to be proportional to x/)'u,, where 7,,., the unstable stacking energy, is a new solid state parameter identified by the analysis. It is the maximum energy encountered in the block-like sliding along a slip plane, in the Burgers vector direction, of one half of a crystal relative to the other. Approximate estimates of ~,~j are summarized and the results are used to evaluate brittle vs ductile response in fcc and bcc metals in terms of the competition between dislocation nucleation and Griffith cleavage at a crack tip. The predictions seem compatible with known behavior and also show that in many cases solids which are predicted to first cleave under pure mode I loading should instead first emit dislocations when that loading includes very small amounts of mode II and III shear. The analysis in this paper also reveals a feature of the near-tip slip distribution corresponding to the saddle point energy configuration for cracks that are loaded below the nucleation threshold, as is of interest for thermal activation.