The Behavior of Screw Dislocations Emitted from a Star Crack with a Central Hole

The behavior of screw dislocations emitted from a star crack with a central hole was investigated using discrete dislocation modeling. Cracks are uniformly distributed along the circumference of a circular hole. Dislocations are assumed to be emitted one by one from the crack tips along the radial direction. Each emitted dislocation moves along the radial direction and its velocity is proportional to the third power of the effective shear stress. A dislocation-free zone exists based on the assumption that the crack tip must overcome an energy barrier to emit a dislocation. The effects of the central hole, slit crack, number of cracks and applied stress on the plastic zone, total number of dislocations emitted from all crack tips and the first crack tip, and the dislocation-free zone were studied for a given friction stress. This revised version was published online in July 2006 with corrections to the Cover Date.     

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.     

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.     

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.     

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。     

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.     

A distributed dislocation stress analysis for crazes and plastic zones at crack tips

A distributed dislocation method is developed to obtain analytically the applied stress as well as the surface stress profile along narrow plastic zones at the tip of a crack in a homogeneous tensile stress field. Replacing the plastic zone by a continuous array of mathematical dislocations, the stress field solution of this mixed boundary value problem (the displacement profile of the plastic zone is fixed while the tensile stresses are zero across the crack) can be solved. A computer program based on this stress field solution has been constructed and tested using the analytical results of the Dugdale model. The method is then applied to determining the surface stress profiles of crazes and plane-stress plastic deformation zones grown from electron microprobe cracks in polystyrene and polycarbonate respectively. The necessary craze and zone surface displacement profiles are determined by quantitative analysis of transmission electron micrographs. The surface stress profiles, which show small stress concentrations at the craze or zone tip falling to an approximately constant value which is maintained to the crack tip, are compared with those previously computed using an approximate Fourier transform method involving estimation of the displacement profile in the crack. The agreement between the approximate method and the exact distributed dislocation method is satisfactory.     

Dynamic observation of dislocation-free plastic deformation in gold thin foils

Ductile fracture of metals produces a thin foil portion, which is observable by transmission electron microscopy, at the fractured edge. The thin foil portion shows unusual deformation microstructure, which contains no dislocations, but contains vacancy-type point defect clusters at extraordinarily high density. Dynamic observation of the deformation process revealed that these defect clusters are produced in the portion of local heavy deformation; however, no dislocation motion was observed during the course of the heavy plastic deformation, constituting direct evidence that the unusual deformation microstructure is produced by plastic deformation without dislocations. Also, the deformation was found to involve 14% elastic deformation, indicating that the dislocation-free plastic deformation occurs under an extraordinarily high internal stress level of more than 10 GPa, which is comparable to the ideal strength of metals. Furthermore, during the dislocation-free plastic deformation, equal-thickness fringes were found to disappear temporarily, suggesting that instability of crystalline state under extraordinarily high internal stress level is a key factor for the mechanism of dislocation-free plastic deformation.     

The condition for the cyclic plastic deformation of the crack tip: the influence of dislocation obstacles

The stress intensity range below which no cyclic plastic deformation at the crack tip and, hence, no fatigue crack propagation occurs is investigated. The emission of dislocations from the crack tip is assumed as mechanism for the dislocation generation. For a mode III crack, a computer simulation is carried out to study the influence of dislocation obstacles. Both the distance between the crack tip and the obstacle and the strength of the obstacle are varied and the characteristic dislocation arrangements are shown.The stress intensity range necessary to return one dislocation to the crack tip is mainly controlled by the critical stress intensity factor sufficient to emit a dislocation. The influence of the obstacles is not very significant.     

A study of the influence of grain boundaries on short crack growth during varying load using a dislocation technique

The propagation of short cracks in the neighbourhood of grain boundaries have been investigated using a technique were the crack is modelled by distributed dislocation dipoles and the plastic deformation is represented by discrete dislocations. Discrete dislocations are emitted from the crack tip as the crack grows. Dislocations can also nucleate at the grain boundaries. The influence on crack growth characteristics of the distance between the initial crack tip and the grain boundary has been studied. It was found that crack growth rate is strongly correlated to the dislocation pile-ups at the grain boundaries.     

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.     

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.     

A theoretical model for the electromagnetic radiation emission during plastic deformation and crack propagation in metallic materials

This paper presents a theoretical model for the electromagnetic radiation (EMR) emissions during plastic deformation and crack propagation in metallic materials. It is shown that under an externally applied stress, edge dislocations within the plastic zone ahead of a crack tip form accelerated electric line dipoles which give rise to the EMR emissions. The dynamic motion of these dislocations becomes overdamped, underdamped or critically damped, depending upon the material/microstructural properties such as mass per unit length of dislocation, line tension, damping coefficient, and distance between the dislocation pinning points. The nature of the EMR signals, viz. exponential decay or damped sinusoidal, is decided essentially by these damping characteristics. The EMR emissions are followed by crack propagation in metallic materials. The EMR has a continuous frequency spectrum with a frequency bandwidth ranging from 10⁸ to 10¹² radians s⁻¹, depending upon the properties of the metals. Screw dislocations do not contribute to the EMR emissions. The paper also presents some experimental results on the EMR emissions in ASTM B265 grade 2 titanium sheets. The nature (damped sinusoidal and exponential decay), amplitude and frequency of the observed EMR emissions are in conformity with the predictions of the theoretical model.     

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     

In-situ Observation of Initiation and Propagation of Cleavage Microcrack in TiAl

Nucleating and propagating of nancrack formed in dislocation free zone (DFZ) for the brittle TiAl alloy has been studied through in-situ tensile test in TEM and analyzed using microfracture mechanics. The resufts show that a lot of dislocations can be emitted from a crack tip when the applied stress intensity Kla i5 larger than the stress intensity for dislocatin emission Kle=1.4 M Pa·m1/2 and a dislocation free zone, which smetimes is a close zone, can form after reaching equilibrium. The DFZ is a elastic zone with large strain and then the stress in the DFZmight equal to the cohesive strength σth because the crack tip is still sharp. When Kla is larger than the stress intensity for nanocrack nucleation Kli =2.4 M Pa·m1/2, the stress within a certain range in the DFZ would equal to σth and then a nanocrack initiates in the DFZ or sometimes at the notch tip. The nanocrack formed in the DFZ is stable and can propagate a small distance in cleavage mode through multiplication and movement of dislocation in the plastic zone, during keeping constant displacement. Increasing Kla can make the crack stably propagate continuously or discontinuously and it means that the stre5s intensity for crack propagation, Klp, is larger than Kli. Therefre, Kle 相似文献   

Damage mechanisms of fatigue fracture in a metastable beta Ti-15-3 alloy

The mechanism of crack tip deformation in metastable beta Ti-15-3 alloy under fatigue loading has been examined. In spite of the small thickness of the test specimens (1 mm), the plastic zone revealed plane strain conditions which was transformed to a plane stress zone when its size became 0.25 of the crack length. Slip processes whose density increased with crack length were the dominant microscopic feature of crack tip plasticity. Microcracks emanating from the main crack appeared as a result of extensive slip damage. Transmission electron microscopy (TEM) and X-ray evidence indicate the absence of twinning or phase transformation and that dislocation processes constitute the microstructural origin of crack propagation resistance in the alloy. Energy calculations show that the specific energy of slip, 20 MJ m⁻³, exceeds that of microcracking by three orders of magnitude.     

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.     

Orientation dependence of fracture in copper bicrystals with symmetric tilt boundaries

Experimental results (Wang and Anderson (1991), Acta Metall. 39, 779–792) show that the fracture behavior of Σ9 copper bicrystals depends on the cracking direction. Near-interface transgranular fracture surfaces were observed in the case of the crack growing in the [ 14] direction, with an essentially ductile failure mode, while the case of the crack growing in the [1 ] direction showed far less toughness and had an intergranular fracture surface with cleavage tongues. Asymptotic and finite element models for stationary cracks in ideally plastic and strain hardening materials have been used to examine this cracking direction dependency from a small strain continuum mechanics point of view. The tensile stress ahead of the crack tip was found to be essentially identical for the two growth directions, with the brittle orientation resulting in only slightly higher stress values at small distances from the crack tip. However, the strain field was found to be different for the two orientations, with the overall plastic zone size being much larger in the ductile case. Also, the orientations of the zones of concentrated shearing ahead of the crack, observed in the ideally plastic model, suggest two different dislocation shearing mechanisms. In the ductile case, this zone is parallel to the slip plane, resulting in a regular shearing mechanism in which dislocations can be nucleated at the crack tip and glide on the (111) slip plane. In contrast, this zone is perpendicular to the (111) slip plane in the brittle case, resulting in a kinking shear mode in which dislocations from other external sources expand in a dipole mode to produce macroscopically concentrated shearing. Thus, apart from the dislocation nucleation considerations, continuum mechanics does not seem to be able to fully explain this difference in directional dependency of fracture in the Σ9 copper bicrystals.     

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.     

Cyclic Saturation Dislocation Pattern Observation in the Vicinity of Grain Boundaries by Electron Channeling Contrast Technique

State Key Laboratory for Fatigue and Fracture of Materials, Institute of Metal Research, Chinese Academy of Sciences,Shenyang, 110015, China)Abstract:The cyclic saturation dislocation patterns within grains and in the vicinity of low-angle grain boundaries in fatigued copper crystal were successfully observed by electron channeling contrast technique in SEM. The results show that the dislocation patterns within grains consisted of typical two-phase structure, i.e. persistent slip bands (PSB) and veins. With increasing plastic strain amplitude (γp1 ≥1.7×10-3), large amount of PSBs and regufar dislocation walls were observed.The dislocation walls and PSBs could cross through the low-angle grain boundaries continuously except that the dislocation-free zone (DFZs) appeared at some local regions. Combining with the cyclic stress-strain response and dislocation patterns, the effect of low-angle grain boundaries on cyclic deformation behavior was discussed.