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.     

Micro-mechanical analysis and TEM study of crack initiation in dislocation free zone

Dislocation emission, dislocation-free zone (DFZ) formation and crack initiation in the DFZ and/or at the crack tip were analyzed by micromechanics. The results show that a DFZ is formed after dislocation emission under constant load. The DFZ size decreases with increase in the applied stress intensity factor K _Ia or lattice friction stress _f. There are two stress peaks ahead of the crack tip. The first one is located at the blunt crack tip and the second one in the DFZ. With increasing in the applied stress intensity factor K _Ia, the peak stress at the crack tip may decrease while the peak stress in the DFZ increases monotonically. Microcrack will initiate when the peak stress is equal to the cohesive strength. In situ tensile tests in a transmission electron microscope (TEM) show that microcrack initiates in DFZ or/and at a blunt crack tip after dislocation emitting and DFZ formation.     

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.     

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   

A new nonlocal cohesive stress law and its applicable range

In this paper, we attempt to provide a new analytical method to determine the cohesive law in the framework of nonlocal continuum mechanics. Firstly, the equivalence between the cohesive stress and the surface-induced traction (nonlocal surface residual) is established on the basis of the nonlocal stress boundary condition. Then a new cohesive stress law is derived logically from the perspective of rational mechanics, which characterizes the dependence of the cohesive stress on the crack opening displacement (COD) within the cohesive zone. Finally, we apply this new cohesive crack model to two fracture examples with different cohesive zone sizes, and investigate the stress field ahead of the crack tip in detail. The results show that the stress singularity at the crack tip is removed, and the maximum stress occurs within the cohesive zone away from the crack tip. Moreover, the stress in the large-scale cohesive zone drops rapidly to a constant approaching zero, exhibiting a stronger softening behavior.     

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.     

A mechanism of void growth in the region of the plastic zone ahead of a crack-tip

The mechanism of void growth in the region of the plastic zone ahead of a crack tip proposed earlier is further developed. As a result of partial annihilation of lattice dislocations representing the plastic zone with elastic dislocations representing the void, ledge steps are formed on the void surface causing void growth. A detailed dislocation model of the mechanism of void growth is illustrated using both the discrete dislocation analysis and the continuous distribution method. The latter is particularly developed to provide the scaling methods, so that the results can be readily obtained for different sizes of the crack and the void as well as for different positions of the void with respect to the crack. Application of these results to void growth in the region of the plastic zone ahead of a crack tip subjected to alternating stresses and creep is also 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.     

A combined dislocation—cohesive zone model for fracture in a confined ductile layer

The collective dislocation behavior near a crack tip in a ductile layer sandwiched between two brittle solids is analyzed via two-dimensional dislocation dynamics (DD) simulations that incorporate a cohesive zone (CZ) model. The cohesive crack tip is treated as part of a much larger finite crack confined in the ductile layer. The underlying boundary value problem is formulated with a set of boundary integral equations and numerically evaluated with a collocation method. The fracture energy of the layered composite material is shown to be strongly correlated with the layer thickness and is directly influenced by the cohesive strength of the ductile layer (Hsia KJ et al. (1994) J Mech Phys Solids 6 877–896).     

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.     

Damage Dependent Constitutive Behavior and Energy Release Rate for a Cohesive Zone in a Thermoviscoelastic Solid

In this paper a cohesive zone is introduced ahead of a crack tip in order to avoid the singularity at the crack tip. By applying thermodynamics to the cohesive zone and the surrounding body, a fracture criterion will be established so that the inelastic energy dissipation both in the cohesive zone and the surrounding bulk material can be distinguished from the energy released by fracture, and the propagation of crack can be predicted. In addition, the cohesive zone constitutive equation is constructed utilizing the Helmholtz free energy in the form of a single hereditary integral for a nonlinear viscoelastic material. The resulting constitutive model for the cohesive zone contains an internal state variable which represents the damage state within the cohesive zone. When the cohesive zone opening displacement is known, the energy release rate is thus history dependent, which is expressed in terms of the damage state, the length of separation in the cohesive zone and the geometric configuration of the cohesive zone opening displacement. Example results contained herein demonstrate this effect. This revised version was published online in July 2006 with corrections to the Cover Date.     

The cohesive zone model in a problem of delayed hydride cracking of zirconium alloys

The crack tip model with the cohesive zone ahead of a finite crack tip has been presented. The estimation of the length of the cohesive zone and the crack tip opening displacement is based on the comparison of the local stress concentration, according to Westergaard's theory, with the cohesive stress. To calculate the cohesive stress, von Mises yield condition at the boundary of the cohesive zone is employed for plane strain and plane stress. The model of the stress distribution with the maximum stress within the cohesive zone is discussed. Local criterion of brittle fracture and modelling of the fracture process zone by cohesive zone were used to describe fracture initiation at the hydride platelet in the process zone ahead of the crack tip. It was shown that the theoretical K _IH-estimation applied to the case of mixed plane condition within the process zone is qualitatively consistent with experimental data for unirradiated Zr-2.5Nb alloy. In the framework of the proposed model, the theoretical value of K ^H _IC for a single hydride platelet at the crack tip has been also estimated.     

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.     

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.     

The cohesive zone model in a problem of delayed hydride cracking of zirconium alloys

The crack tip model with the cohesive zone ahead of a finite crack tip has been presented. The estimation of the length of the cohesive zone and the crack tip opening displacement is based on the comparison of the local stress concentration, according to Westergaard's theory, with the cohesive stress. To calculate the cohesive stress, von Mises yield condition at the boundary of the cohesive zone is employed for plane strain and plane stress. The model of the stress distribution with the maximum stress within the cohesive zone is discussed. Local criterion of brittle fracture and modelling of the fracture process zone by cohesive zone were used to describe fracture initiation at the hydride platelet in the process zone ahead of the crack tip. It was shown that the theoretical K _IH-estimation applied to the case of mixed plane condition within the process zone is qualitatively consistent with experimental data for unirradiated Zr-2.5Nb alloy. In the framework of the proposed model, the theoretical value of K ^H _IC for a single hydride platelet at the crack tip has been also estimated.     

Discrete dislocation analysis and path dependent plasticity

The discrete dislocation method has been applied in order to determine the path dependent plasticity and work hardening associated with the formation of a plastic zone at the tip of a crack in a semi-ductile or ductile material. The constitutive equations connecting the energy terms contributing to the total energy of a plastic crack are derived and the crack extension force, or J integral, is expressed in a simple form in terms of these energy terms. The deficiencies in the continuum mechanical approach in analyzing stably growing cracks under incremental loading conditions are pointed out and the merits of discrete dislocation analysis in overcoming these deficiencies are illustrated. The results of discrete dislocation analysis are used to obtain both a microscopic and macroscopic perspective of the fracture processes.     

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.     

Zn单晶解理裂纹前端的范性行为

用蚀坑法观察了 Zn 单晶解理裂纹前端位错。结果表明,裂纹前端位错密度分布具有 DFZ模型预言的特征,且裂纹尖端与第一个位错的距离 X_1(即 DFZ 值)以及范性区位错数 N 均与根据Majumdar 和 Burns 的 DFZ 理论推算数值吻合较好。在此基础上,对裂纹前端发射位错和位错屏蔽裂纹前端等问题作了讨论。     

低合金高强度钢的微观组织和疲劳裂纹扩展行为

用透射电镜观察了３０ＣｒＭｎＳｉＮｉ２Ａ钢等温的微观组织，疲劳裂纹扩展行为、裂纹尖端塑性区和位错结构，结果表明，等温状态组织由马氏体和贝氏体组成。在一个奥氏体晶粒内一般存在四个板条领域、裂纹尖端的塑性区内存在主位错带，疲劳断裂的基本组织单元为板条晶或板条束。裂纹遇到板条束界时方向发生较大偏斜。