Dislocation Behaviour near the Crack Tip in Bulk Fe-3% Si Single Crystal

An investigation has been made of the disloca-tion distribution and dislocation free zone near thecrack tip in bulk Fe-3% Si single crystal duringdeformation in SEM.It has been found that anumber of dislocations were emitted from the cracktip during deformation.After that,the dislocationsmoved rapidly away from the crack tip,which indi-cated that they were strongly repelled by the stressfield at the crack tip.Between the crack tip and theplastic zone there is a region of dislocation-free,which is referred to as dislocation-free zone (DFZ).The length of DFZs is roughly estimated 100μm which is much longer than that found in thinfoil specimen.The variation of dislocation densityas a function of the distance from the crack tip wasmeasured,which showed that the dislocations areinversely piled up in the plastic zone.The length ofDFZs increased with both the length of pre-crackand the amplitude of applied stress.     

Distribution of dislocations at a mode I crack tip and their shielding effect

Distribution of dislocations at a finite mode I crack tip is formulated. Closed form solutions for the dislocation distribution function, the dislocation-free zone (DFZ), the local stress intensity factor and the crack tip stress field are obtained. The dislocation distribution has similar features to a mode III crack model. Under a given applied stress, there may exist different configurations of plastic zone and DFZ. Crack tip shielding by dislocations depends on both applied stresses and the configuration.     

Dislocations at ductile/plastic crack tips: in-situ TEM observations

 In-situ observations of dislocation structures ahead of crack tips in TEM metal foils are reviewed. Two cases are compared in particular: Structure development during in-situ straining to failure of (i) electron-transparent foils ahead of the tip of a growing crack that spreads from the thinnest regions or perforations and (ii) initially non-transparent thick foils. In the latter case cracks formed only after substantial in-situ straining, and they propagated along dislocation cell walls via repeated stimulated crack nucleation ahead of the tip. This behavior was shown to adequately simulate bulk behavior and such cracks do not exhibit dislocation-free zones at their tips. By contrast, dislocation-free regions along ligaments formed by crack propagation and observed in thin (e.g. about 100 nm or less) TEM foils are found to be artifacts due to strong dislocation image forces. These image forces at the same time limit mutual dislocation interactions to the thickness of the foil, and rotate the dislocations to be normal to the foil plane, meanwhile straightening them. This behavior has no correspondence to conditions at real cracks in bulk materials. Theoretical expressions are derived for the dislocation densities ahead of crack tips that give rise to long-range and shorter range stress fields in mode I crack tip configurations, respectively. Received:19 December 1997 / Accepted: 22 December 1997     

Edge dislocations near a cracked sliding interface

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. This revised version was published online in August 2006 with corrections to the Cover Date.     

Inclined pileup of screw dislocations at the crack tip with a dislocation-free zone

A single pileup of screw dislocations extending from the crack tip along an inclined direction has been observed in experiments. It is often associated with dislocation emission mechanisms at the crack tip. This linear pileup is a microplastic slipline emanating from the crack tip. A region near the crack tip is often free from dislocations because of a finite resistance value for the crack tip to emit dislocations. The mathematical problem is solved in this paper by applying the extended Wiener-Hopf method. The condition of finite stress at the end of the plastic zone, the crack opening displacement, and the stress distribution along the slipline are obtained in analytical expressions. Numerical values are calculated and the results can be used to discuss brittle versus ductile fracture for metals as treated in previous studies. A method to approximately calculate the corresponding results for edge dislocations is suggested.     

Elastic interaction between screw dislocations and the internal crack near a free surface

The elastic interaction between screw dislocation and the internal crack near a free surface has been investigated. The stress intensity factor at the crack tip, crack extension force, the image force on the dislocation are affected by the free surface. The number and nature of dislocations, m, inside the crack also play an important role in fracture. In order to understand the plastic zone, the zero-force points of dislocation along the x-axis are involved. The dislocation emitted from the right-hand crack tip is enhanced by positive m and reduced by negative m. On the other hand, if the internal crack is closer to the free surface, a dislocation generated from the right-hand crack tip is easier for negative m and more difficult for positive m. However, the role of m on the dislocation emission for the left-hand crack tip is opposite to that for the right-hand crack tip. Finally, three special cases can be obtained from our results. (1) The interaction between a dislocation and a surface crack; (2) the interaction between a dislocation and an internal crack; (3) the interaction between two dislocations.     

The elastic interaction of screw dislocations and a star crack with a central hole

The elastic interaction of screw dislocations and a star crack with a central hole was investigated. The complex potential of the present problem was obtained from that of an internal crack in an infinite medium using the conformal mapping technique. The stress field, image force and strain energy of dislocation, and stress intensity factor at the crack tip were derived. The critical stress intensity factor for dislocation emission was calculated based on the spontaneous dislocation emission criterion. The influence of the ratio of crack length to hole radius, crack number, and dislocation source on the above mechanical variables were studied. The present solution was reduced to several special cases previously reported in the literature.     

TEM observations of dislocation emission at crack tips in aluminium

Direct observations were made of the propagation of ductile cracks and associated dislocation behaviour at crack tips in aluminium during tensile deformation in an electron microscope. In the electropolished area, the cracks propagated as a Mode III shear-type by emitting screw dislocations on a plane coplanar to the crack plane. A zone free of dislocations was observed between the crack tip and the plastic zone. As the cracks propagated into thicker areas, the fracture mode changed from Mode III to predominantly Mode I. The crack top of the Mode I cracks was blunted by emitting edge dislocations on planes inclined to the crack plane. The blunted cracks did not propagate until the area ahead of the crack tip was sufficiently thinned by plastic deformation. The cracks then propagated abruptly, apparently without emitting dislocations. The stress intensity factor was measured from the crack tip geometry of Mode III cracks and it was found to be in good agreement with the critical value of the stress intensity factor required for dislocation generation.     

NUCLEATION,BLUNTING OR PROPAGATION OF A NANOCRACK IN DISLOCATION-FREE ZONES OF THIN CRYSTALS

Nucleation, blunting and propagation of nanocracks in dislocation-free zones (DFZs) ahead of crack tips in ductile and brittle metals have been investigated by tensioning in situ with a TEM, and analysed using microfracture mechanics. The results show that in either ductile or brittle metals, many dislocations could be emitted from a loaded crack tip and a DFZ formed after equilibrium. The stress in the DFZ may be up to the cohesive strength of the material, and then a nanocrack is initiated in the DFZ or directly from the crack tip. In ductile metals, the nanocrack is blunted into a void or notch during constant displacement. In brittle metals, the nanocrack propagated as a cleavage microcrack rather than being blunted.     

On the contact zone of a subinterfacial Zener-Stroh crack

Summary A Zener-Stroh crack is initiated by dislocations pile-up. Due to this displacement loading mechanism, only one of the two crack tips is sharp, and crack propagation is possible along the sharp tip only. When such a crack is initiated near an interface, the crack faces behind the sharp crack tip may contact each other due to material mismatch and loading combination. In the present study, a subinterface Zener-Stroh crack is analyzed with contact zone consideration near the tip. The problem is formulated as a set of nonlinear Cauchy-type singular integral equations which are solved numerically using Erdogan and Gupta's method. The physically pathological features of interpenetration of the crack surfaces and oscillation of the near tip fields are eliminated in the solutions due to the presence of a contact zone near the crack tip. It is found that the normal traction is bounded at the crack tip where a contact zone exists; while the shear traction has square-root singularities at both the crack tips. This result, is totally different to the case of an interface crack where Mode I and Mode II stress intensity factors, are inter-related at the sharp crack tip.     

A Griffith crack shielded by a dislocation pile-up

The dislocation free zone at the tip of a mode III shear crack is analyzed. A pile-up of screw dislocations parallel to the crack front, in anti-plane shear, in the stress field of a crack has been solved using a continuous distribution of dislocations. The crack tip remains sharp and is assumed to satisfy Griffith's fracture criteria using the local crack tip stress intensity factor. The dislocation pile-up shield the sharp crack tip from the applied stress intensity factor by simple addition of each dislocation's negative contribution to the applied stress intensity value. The analysis differs substantially from the well known BCS theory in that the local crack tip fracture criteria enters into the dislocation distributions found.     

Thermal stress singularities at tips of a crack in a semi-infinite medium under uniform heat flow

In the framework of plane thermoelastic problems is discussed the thermal stress field near the tips of an arbitrarily inclined crack in an isotropic semi-infinite medium with the thermally insulated edge surface under uniform heat flow. The crack is replaced by continuous distributions of quasi-Volterra dislocations corresponding to line heat sources and edge dislocations, and we obtain a set of simultaneous singular integral equations for dislocation density functions, whose solution is given in the forms of series in terms of Tchebycheff polynomials of the first kind. By means of this method, the thermal stress singularities at the crack tips are estimated exactly and the stress intensity factors can be readily evaluated. Numerical results are given for the particular case where the surface of the inclined crack is maintained at constant temperature and the heat supplied across the surface of the crack vanishes as a whole. The effects of the distance from the crack tip to the edge surface of the semi-infinite medium and the angle of inclination of the crack on the stress intensity factors and the initial direction of crack extension are shown graphically.     

On the representation of solutions for the theory of generalized thermoelasticity with three phase-lags

An analytical investigation on the plastic zone size (PZS) of a crack near a circular inclusion has been carried out. Both the crack and the circular inclusion are embedded in an infinite matrix, with the crack oriented along the radial direction of the inclusion. In the solution procedure, the crack is simulated as a continuous distribution of edge dislocations. With the Dugdale model of small scale yielding, two stripe plastic zones at both crack tips are introduced. Using the solution of a circular inclusion interacting with a single dislocation as the Green’s function, the physical problem is formulated as a set of singular integral equations. With the aid of Erdogan and Gupta’s method and iterative numerical procedures, the singular integral equations are solved numerically for the PZS and the crack tip opening displacement. The results obtained in the current work can be reduced to those simpler cases of the Dugdale model.     

On the plastic zone size and CTOD study for a Zener�CStroh crack interacting with a circular inclusion

An analytical solution is given for plastic yielding of a Zener?CStroh crack near a circular inclusion embedded in an infinite matrix. The crack is orientated along the radial direction of the inclusion. In the solution procedure, the crack is simulated as a continuous distribution of edge dislocations. Using the Dugdale model of small-scale yielding, plastic zones are introduced at both crack tips. Using the solution of a circular inclusion, interacting with a single dislocation as the Green??s function, the physical problem is formulated into a set of singular integral equations. With the aid of Erdogan??s method and iterative numerical procedures, the singular integral equations are solved numerically for the plastic zone sizes and crack tip opening displacement. The results obtained in the current work are verified by reduction to simpler cases of the Dugdale model. Various parameters such as the distance, shear modulus ratio, Poisson??s ratio, and loading condition are studied.     

The DFZ model of fracture at crack tip and crack initiation criterion

Direct observation by transmission electron microscopy (TEM) has been made on the distribution of dislocations in front of the crack tip during tensile deformation of aluminum. A microfracture model has been established to describe the equilibrium configuration of the dislocations in the presence of a dislocation-free zone (DFZ). The site of void nucleation observed from TEM experiments was found to be at about the place of maximum dislocation density predicted from the model. The relationship between the size of crack, DFZ and crack opening displacement (COD) was obtained as a function for a crack initiation criterion.     

ODS铁素体钢中微裂纹形核过程的TEM原位观察

采用透射电子显微镜原位位伸范膜试样法研究了ＯＤＳ铁素体钢中位错发射及微裂纹形核，钝化和扩展的过程。结果表明，ＯＤＳ铁素体钢在原位拉伸时，裂尖首先发出大量位错并形成无位错区，保持恒位移，纳米级微裂纹在裂纹顶端连贯形核或在ＤＦＺ中不连续形核，这个微裂纹并不钝化成孔洞。     

Nucleation and Blunting of Nanocracks in Brass

In situ tensile test of brass foil specimens in TEM shows that many dislocations were emitted from a loaded crack tip and a dislocation free zone (DFZ) was formed under condition of constant displacement. The DFZ is an elastic zone, where the stress may equal to the cohesive strength th when the applied stress is high enough. As a result, nanocracks would initiate discontinuously in the DFZ or, sometimes, at a blunted-crack tip. As soon as the nanocrack nucleated, it quickly blunts into a void, which results in ductile fracture.     

A unified model for dislocation nucleation, dislocation emission and dislocation free zone

In this paper, a unified model for dislocation nucleation, emission and dislocation free zone is proposed based on the Peierls framework. Three regions are identified ahead of the crack tip. The emitted dislocations, located away from the crack tip in the form of an inverse pileup, define the plastic zone. Between that zone and the cohesive zone immediately ahead of the crack tip, there is a dislocation free zone. With the stress field and the dislocation density field in the cohesive zone and plastic zone being, respectively, expressed in the first and second Chebyshev polynomial series, and the opening and slip displacements in trigonometric series, a set of nonlinear algebraic equations can be obtained and solved with the Newton-Raphson Method. The results of calculations for pure shearing and combined tension and shear loading after dislocation emission are given in detail. An approximate treatment of the dynamic effects of the dislocation emission is also developed in this paper, and the calculation results are in good agreement with those of molecular dynamics simulations.Presented at the Far East Fracture Group (FEFG) International Symposium on Fracture and Strength of Solids, 4–7 July 1994 in Xi'an, China.     

Transient dislocation emission from a crack tip in an anisotropic elastic material

The emission of a dislocation with a general Burgers vector from the tip of a stationary semi-infinite crack in an anisotropic elastic material is examined. The dislocation is assumed to leave the crack tip along the crack extension plane at constant speed. Explicit expressions for the transient shielding stress intensity factors at the crack tip and the drag forces on the dislocations are derived. Numerical results for a class of cubic materials and two hexagonal crystals, zinc and cobalt, are given. Dislocation emission under plane stress wave loading is discussed.     

DISLOCATION-FREE ZONE AHEAD OF CRACK-TIP IN METALS

本文对材料断裂研究中的裂纹尖端形变行为,特别是裂纹尖端无位错区的研究作了简要评述。其中包括:一些薄膜金属,如Al,Cu,Nb,Fe,W 和Mo 等,裂纹尖端在变形时的位错发射和无位错区存在的实验事实;裂纹尖端位错的屏蔽与反屏蔽概念的引进;材料断裂研究中无位错区模型的引进和描述;延-脆断裂转变的判据。