The effects of residual stress on fatigue behavior and crack propagation from laser shock processing-worked hole

Laser shock processing (LSP) is used to enhance the fatigue behavior of the structures. The effects of residual stress on fatigue behavior and crack propagation from LSP-worked hole were performed in this investigation. The influence of compressive stress on fatigue behavior and crack propagation of the hole was revealed, and a parametric study on residual stress and stress intensity factor was performed in order to determine their effect on crack growth propagation. The dislocation microstructure of 7050 aluminum at different laser intensities shows similar results, which indicated that LSP had an obvious inhibitory action to fatigue crack initiation and growth of the hole crack.     

The interaction between screw dislocations and an interfacial blunt crack and a sharp crack

The interaction between screw dislocations and an interfacial blunt crack and a sharp crack under loads at infinity is dealt with. Utilizing the Muskhelishvili complex variable method, the closed form solutions are derived. 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 decreases with the increase of dislocation azimuth. The critical loads at infinity for dislocation emission increase with the increment of the emission angle and the distance.     

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 weight function method for mixed modes hole‐edge cracks

A weight function approach is proposed to calculate the stress intensity factor and crack opening displacement for cracks emanating from a circular hole in an infinite sheet subjected to mixed modes load. The weight function for a pure mode II hole‐edge crack is given in this paper. The stress intensity factors for a mixed modes hole‐edge crack are obtained by using the present mode II weight function and existing mode I Green (weight) function for a hole‐edge crack. Without complex derivation, the weight functions for a single hole‐edge crack and a centre crack in infinite sheets are used to study 2 unequal‐length hole‐edge cracks. The stress intensity factor and crack opening displacement obtained from the present weight function method are compared well with available results from literature and finite element analysis. Compared with the alternative methods, the present weight function approach is simple, accurate, efficient, and versatile in calculating the stress intensity factor and crack opening displacement.     

Molecular Dynamics Simulation of Porous Layer-enhanced Dislocation Emission and Crack Propagation in Iron Crystal

The internal stress induced by a porous layer or passive layer can assist the applied stress to promote dislocation emission and crack propagation, e.g. when the pipeline steel is buried in the soil containing water, resulting in stress corrosion cracking (SCC). Molecular dynamics (MD) simulation is performed to study the process of dislocation emission and crack propagation in a slab of Fe crystal with and without a porous layer on the surface of the crack. The results show that when there is a porous layer on the surface of the crack, the tensile stress induced by the porous layer can superimpose on the external applied stress and then assist the applied stress to initiate crack tip dislocation emission under lowered stress intensity KI, or stress. To respond to the corrosion accelerated dislocation emission and motion, the crack begins to propagate under lowered stress intensity KI, resulting in SCC.     

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.     

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.     

氢对裂尖释放位错临界应力强度因子K_e和无位错区DFZ的影响

理论计算得出:氢降低位错运动点阵阻力,使得裂尖释放位错临界应力强度因子降低;氢的存在使裂尖所释放的位错受到附加吸引力,缩短了 DFZ。TEM 原位拉伸实验表明(i)在氢气氛中,纯铁裂尖位错释放的临界应力强度因子降低。(ii)对 Fe-3%Si 单晶体,电解充氢后裂尖DFZ 消失。(iii)Fe-3%Si 多晶体预形变后充氢,裂尖存在 DFZ。实验结果证实了作者提出的理论模型。     

Dislocation and point-force-based approach to the special Green's Function BEM for elliptic hole and crack problems in two dimensions

In this paper we give the theoretical foundation for a dislocation and point-force-based approach to the special Green's function boundary element method and formulate, as an example, the special Green's function boundary element method for elliptic hole and crack problems. The crack is treated as a particular case of the elliptic hole. We adopt a physical interpretation of Somigliana's identity and formulate the boundary element method in terms of distributions of point forces and dislocation dipoles in the infinite domain with an elliptic hole. There is no need to model the hole by the boundary elements since the traction free boundary condition there for the point force and the dislocation dipole is automatically satisfied. The Green's functions are derived following the Muskhelishvili complex variable formalism and the boundary element method is formulated using complex variables. All the boundary integrals, including the formula for the stress intensity factor for the crack, are evaluated analytically to give a simple yet accurate special Green's function boundary element method. The numerical results obtained for the stress concentration and intensity factors are extremely accurate. © 1997 John Wiley & Sons, Ltd.     

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.     

Micro-crack initiation at the tip of a semi-infinite rigid line inhomogeneity in piezoelectric solids

A dislocation emission mechanism for micro-crack initiation at the tip of a semi-infinite rigid line inhomogeneity in a piezoelectric solid is proposed in the present paper. For a rigid line inhomogeneity embedded in a piezoelectric matrix, dislocations of one sign are driven away from the tip due to high stress level, while the stationary dislocations of the opposite sign are left behind near the tip of the inhomogeneity. As a result, a micro-Zener–Stroh crack is initiated ahead of the line inhomogeneity. In the current study, a dislocation pileup mechanism for micro-crack initiation at the inhomogeneity tip is proposed. An interesting result is that the critical stress intensity factors for a line inhomogeneity perpendicular to the poling direction can be related to the fracture toughness of a conventional crack in the same material. Analytical solutions show that the critical plane shear stress intensity factor depends on the plane shear mechanical and displacement loadings, and the critical opening stress and electric displacement intensity factors depend on not only the mechanical and displacement loadings, but the electric field and displacement loadings as well.     

The Interaction between a Piezoelectric Screw Dislocation Dipole and an Elliptic Blunt Crack in Elliptical Inhomogeneity

The interaction problem of a piezoelectric screw dislocation dipole with a confocal elliptic blunt crack in elliptical inhomogeneity subjected to remote anti-plane stress field and in-plane electric field is investigated by using the complex method of elasticity. The exact closed-form solutions of a series of quantities, such as singularity stress field, image force and image torque acting on the center of screw dislocation dipole, stress intensity factor and electric displacement intensity factor of crack tip, energy release rate, and generalized strain energy density are obtained. Then the influence laws of remote load, the dip angle of dislocation dipole, the size of blunt crack, and the material constants on the quantities are analyzed. The numerical results show that the image force, image torque, stress intensity factor, and electric displacement intensity factor make periodic variation as the dip angle of dislocation dipole; the energy release rate of crack tip is negative when subjected to pure electric field, however, it can be positive or negative when subjected to the combined action of mechanical field and electric field; the sharp crack is not easy to expand in some combined action of mechanical field and electric field.     

Screw dislocation in the two-phase isotropic thin film of an interfacial crack

The screw dislocation in the two-phase isotropic thin film of an interfacial crack has been investigated. The stress field, stress intensity factors at the crack tip and for dislocation emission, crack extension force, strain energy and the image force on the dislocation are obtained and found to be related to the thickness and effective shear modulus. The effect of size on fracture is pronounced when the thickness is smaller than the distance between dislocation and crack tip by a factor of 1000. The effect of the second phase on fracture is pronounced when μ⁽²⁾/μ⁽¹⁾ is in the range from 0.01 to 100. Newton's third law is proved to be valid for any thickness and shear modulus ratio. This result can be reduced to three special cases.     

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.     

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.     

Is a crack an effective stress riser for triggering of plasticity?

From the stress intensity factors induced by a circular loop attached to a crack front, the resulting image force acting on the dislocation was calculated. The relaxation of the elastic energy stored due to neighbouring surfaces is obtained through integration of the variation of the image force while shifting the loop towards the inside of the material. The amount of relaxation, as numerically determined in this paper under a given loading, is too small to sufficiently decrease the energy barrier for triggering of dislocation emission. Homogeneous nucleation on a perfect crack front is impossible. Since dislocation emission has been experimentally observed under the loading considered, it must come from defects along the crack front.     

Effect of cooperative grain boundary sliding and migration on dislocation emitting from a semi-elliptical blunt crack tip in nanocrystalline solids

A theoretical model is established to investigate the interaction between the cooperative grain boundary (GB) sliding and migration and a semi-elliptical blunt crack in deformed nanocrystalline materials. By using the complex variable method, the effect of two disclination dipoles produced by the cooperative GB sliding and migration process on the emission of lattice dislocations from a semi-elliptical blunt crack tip is explored. Closed-form solutions for the stress field and the force acting on the dislocation are obtained in complex form, and the critical stress intensity factors for the first dislocation emission from a blunt crack under mode I and mode II loadings are calculated. Then, the influence of disclination strength, curvature radius of blunt crack tip, crack length, locations and geometry of disclination dipoles, and grain size on the critical stress intensity factors is presented detailedly. It is shown that the cooperative GB sliding and migration and the grain size have significant influence on the dislocation emission from a blunt crack tip.     

Electro-elastic stress analysis for a wedge-shaped crack interacting with a screw dislocation in piezoelectric solid

The electro-elastic stress investigation on the interaction problem of a screw dislocation near the tip of a semi-infinite wedge-shaped crack in piezoelectric material has been carried out. Explicit closed-form analytical solutions are obtained for the stress intensity factor (SIF) and the electric displacement intensity factor (EDIF) of the crack, as well as the force on dislocation. The derivation is based on the conformal mapping method and the perturbation technique. The dislocation has Burger's vector normal to the isotropic basal plane, with a line force and a line charge being applied at the core of the dislocation. The influence of the location and the wedge angle of the crack on the image force of the dislocation has been discussed in detail. At the same time the effect of the dislocation on the crack behavior has been also examined under different configurations. Two types of PZT materials are used to numerically illustrate the influences of the wedge angle and the location of the dislocation on the image force and the crack intensities. Results obtained in the current study can be fully reduced to various special cases available in the literatures.     

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.     

Microcrack initiation at tip of a rigid line inhomogeneity

A dislocation emission mechanism for microcrack initiation at tip of a rigid line inhomogeneity is proposed in the present paper. For a rigid line inhomogeneity embedded in a ductile matrix, it has been observed that dislocations of one sign are driven away from the tip due to high stress level; while the stationary dislocations of the opposite sign are left behind near the tip of the line inhomogeneity. As the result, a Zener-Stroh crack is initiated at the tip of the inhomogeneity. A very interesting and important result that emerged from the analysis is that the critical stress intensity factor for a line inhomogeneity can be related to the fracture toughness of a crack in the same material.