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

Elastic interaction between screw dislocations and collinear edge and internal cracks

Using the conformai mapping technique, the elastic interaction between a screw dislocation and an internal crack in a thin plate material is investigated. The stress field, the stress intensity factor at the crack tip, and the force on the dislocation are derived. The stress intensity factor at the crack tip is dependent on the positions of the lattice screw dislocations, the dislocations inside the crack, the applied stress and the geometry of the medium. From the image force, the zero‐force points between the crack tip and free surface are obtained. The number of zero‐force points varies from one to five depending on the applied stress and dislocations inside the internal crack. Finally, our results can be reduced to several special cases.

Elastic interaction between screw dislocations and a welded surface crack in composite materials

Based on the solution of an internal crack, we have investigated the elastic interaction of a screw dislocation and cracks emanating from an elliptic hole by using a conformal mapping technique. We have derived the stress field, the image force on the dislocation, the stress intensity factor at the crack tip, and the crack extension force. From the image force, we find the unstable equilibrium positions of dislocation. It is possible to form a plastic zone from the region containing the unstable equilibrium position by collecting dislocations. By extending the concept of the unstable equilibrium position, we also develop the dislocation emission criterion. It is found that the critical applied stress for dislocation emission is dependent on the geometry of the crack. In addition, we also find that the elliptic hole prefers to emanate double cracks. Finally, it is worthwhile to mention that the mapping function cannot be arbitrarily chosen.

On the basis of the results of Lin et al. [12], the interaction between screw dislocations and an internal crack in a two‐phase medium is analyzed. The complex potential, stress field, stress intensity factor, crack extension force and strain energy are derived. The mechanical behavior of the medium is strongly influenced by the shear modulus ratio of the two‐phase medium and the dislocations inside the internal crack. Finally, our results can be reduced to several special cases.

The elastic interaction between screw dislocations and two collinear internal cracks of different length has been investigated by the dislocation modeling method. The dislocation distribution to simulate the cracks and the stress field are obtained. From the stress field, the stress intensity factor at the crack tip and the image force on the dislocation have been derived. The dislocations inside the crack also play an important role in fracture. Newton’s third law is satisfied in this system. Finally, three special cases are discussed.

Screw dislocations near a subsurface crack in a thin plate

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

Screw dislocations near a crack penetrating through an interface

Two types of synchrotron radiation computed tomography (SR‐CT)—projection CT (micro‐CT) and phase‐contrast imaging CT (nano‐CT)—were used to observe internal fatigue cracks in (α + β) Ti‐6Al‐4V alloy. Micro‐CT detected cracks in the specimen at ~1 μm spatial resolution, and the nano‐CT provided magnified images at ~200 nm spatial resolution. The crack initiation sites were clarified as the α‐phase for both the surface and internal cracks; however, their opening behaviors differed. A sharp crack tip was observed in the surface crack, and the crack tip opening displacement (CTOD) increased with an increase in the applied load. By contrast, a blunted crack tip, similar to that of a crack in a vacuum, was observed for the internal crack, and its CTOD remained almost constant regardless of the applied load. These phenomena are likely to explain the different behaviors of surface and internal cracks, particularly the slower growth rate of internal cracks, which leads to a longer fatigue life in the very high cycle fatigue regime.

Elastic behavior of dislocation dipoles near a blunt crack

This paper describes a new stress-intensity factor (SIF) solution for an internal surface crack in a sphere that expands capabilities for this common pressure vessel geometry. The SIF solution employs the weight function (WF) methodology that enables rapid calculations of SIF values. The WF methodology determines SIF values from the nonlinear stress variations extracted in the uncracked geometry, e.g., from service stresses and/or residual stresses. The current approach supports two degrees of freedom that denote the two crack tips located at the deepest location and the surface of the sphere. The geometric formulation of this solution enforces an elliptical crack front, maintains normality of the crack front with the free surface, avoids non-physical crack shapes with protruding “ears”, and supports two degrees of freedom for fatigue crack growth from an internal crack tip and a surface crack tip. The new SIF solution enables all spherical geometries with the exterior diameter greater than or equal to four times the thickness. This WF SIF solution has been combined with stress variations common for spherical pressures vessels: internal pressure on the interior surface, uniform tension on the crack plane, and bending on the crack plane. These stress variations facilitate solution usability. This work builds on earlier efforts for an external surface crack (PVP2021-61397[1]) and provides a comprehensive solution capability for spheres. This paper provides a complete overview of this solution. We present for the first time the geometric formulation of the crack front that enables the new functionality and set the geometric limits of the solution, e.g., the maximum size and shape of the crack front. The paper discusses the bivariant WF formulation used to define the SIF solution and details the finite element (FE) analyses employed to calibrate terms in the WF formulation. A summary of verification efforts demonstrates the credibility of this solution against independent results from FE analyses. We also compare results of this new solution against independent SIFs computed by FE analyses, legacy SIF solutions, API 579, and FITNET. These comparisons indicate that the new WF solution compares favorably with results from FE analyses. Finally, we summarize the capabilities of this solution in NASGRO®.

This paper describes a new stress-intensity factor (SIF) solution for an external surface crack in a sphere that expands capabilities previously available for this common pressure vessel geometry. The SIF solution employs the weight function (WF) methodology that enables rapid calculations of SIF values. The WF methodology determines SIF values from the nonlinear stress variations computed for the uncracked geometry, e.g., from service stresses and/or residual stresses. The current approach supports two degrees of freedom that denote the two crack tips located normal to the surface and the surface of the sphere. The geometric formulation of this solution enforces an elliptical crack front, maintains normality of the crack front with the free surface, and supports two degrees of freedom for fatigue crack growth from an internal crack tip and a surface crack tip. The new SIF solution accommodates spherical geometries with an exterior diameter greater than or equal to four times the thickness. This WF SIF solution has been combined with stress variations common for spherical pressure vessels: uniform internal pressure on the interior surface, uniform tension on the crack plane, and uniform bending on the crack plane. This paper provides a complete overview of this solution. We present for the first time the geometric formulation of the crack front that enables the new functionality and set the geometric limits of the solution, e.g., the maximum size and shape of the crack front. The paper discusses the bivariant WF formulation used to define the SIF solution and details the finite element analyses employed to calibrate terms in the WF formulation. A summary of preliminary verification efforts demonstrates the credibility of this solution against independent results from finite element analyses. We also compare results of this new solution against independent SIFs computed by finite element analyses, legacy SIF solutions, API 579, and FITNET. These comparisons indicate that the new WF solution compares favorably with results from finite element analyses. This paper summarizes ongoing efforts to improve and extend this solution, including formal verification and development of an internal surface crack model. Finally, we discuss the capabilities of this solution’s implementation in NASGRO® v10.0.

Elastic interaction between screw dislocations and a microcrack near an elliptic hole

A stress analysis of a circular hole is one of the classical problems in mechanics. Internal cracks are inherent properties of materials, and they are mostly three-dimensional in form. However, studies on hole problems with three-dimensional internal cracks are still lacking. In this paper, internal cracks were generated in brittle materials containing circular holes based on 3D internal laser-engraved crack technology. Then, uniaxial compression tests were performed. The experimental results were compared with the existing literature, and theoretical and numerical simulation studies were carried out. The results show that: (1) The main crack shapes are the primary cracks and remote cracks. (2) The dynamic fracture characteristics existed in the formation of primary cracks and the surface of remote cracks. The tips of primary cracks were arc-shaped, and the surfaces of the remote cracks were curved. Remote cracks were tangential to the orifice where type III spear-like characteristics appeared. (3) The stress birefringence technology can be combined with 3D internal laser-engraved crack technology for internal crack stress information monitoring, the moire around the orifice was “flamboyant”, and the moire at the tip of the prefabricated crack was “petallike”. (4) The existence of internal cracks reduced the cracking and breaking load of the specimen, and compared with the intact orifice specimen, the upper primary crack, the lower primary crack, the remote crack and the failure load were reduced by 41.2%, 31.7%, 15.9%, and 32.3%, respectively. (5) The results of qualitative stress analysis of the orifice specimen were consistent with the initiation law of primary cracks and remote cracks. The K distribution based on M integral and the numerical simulation of crack propagation process based on the maximum tensile stress criterion were consistent with the law of primary crack growth. Compared with the current mainstream method of transparent rock research, 3D internal laser-engraved crack technology has certain advantages in terms of brittleness, crack authenticity, stress field visualization, and fracture characteristics, and the result will provide experimental and theoretical references for research on three-dimensional problems and internal cracks in fracture mechanics.