Kinetics Of Dislocation Emission From Crack Tips And The Brittle To Ductile Transition Of Cleavage Fracture.

1995 ◽  
Vol 409 ◽  
Author(s):  
A.S. Argon ◽  
G. Xu ◽  
M. Ortiz
Keyword(s):  
Crack Tip ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Cleavage Crack ◽  
Dislocation Emission ◽  
Brittle To Ductile Transition ◽  
Central Elements ◽  
Crack Tips ◽  
Inclined Planes ◽  
Kinetics Of

AbstractSeveral activation configurations of dislocation embryos emanating from cleavage crack tips at the verge of propagating have been analyzed in detail by the variational boundary integral method, as central elements of the rate controlling process of nucleation governed fracture transitions from brittle cleavage to tough forms, as in the case for BCC transition metals. The configurations include those on inclined planes, oblique planes and crack tip cleavage ledges. Surface ledge production resistance is found to have a very strong embrittling effect. Only nucleation on oblique planes near a free surface and at crack tip cleavage ledges are found to be energetically feasible to explain brittle-to-ductile transition temperatures in the experimentally observed ranges.

Mechanisms of Intergranular Fracture

1998 ◽  
Vol 539 ◽  
Author(s):  
Diana Farkas
Keyword(s):  
Grain Boundary ◽  
Crack Tip ◽  
Boundary Region ◽  
Failure Behavior ◽  
Cleavage Crack ◽  
Quasi Equilibrium ◽  
Dislocation Emission ◽  
Embedded Atom ◽  
Crack Tips ◽  
Ductile Behavior

AbstractWe present a study of the atomistic mechanisms of crack propagation along grain boundaries in metals and alloys. The failure behavior showing cleavage crack growth and/or crack-tip dislocation emission is demonstrated using atomistic simulations for an embedded-atom model. The simulations follow the quasi-equilibrium growth of a crack as the stress intensity applied increases. Dislocations emitted from crack tips normally blunt the crack and inhibit cleavage, inducing ductile behavior. When the emitted dislocations stay near the crack tip (sessile dislocations), they do blunt the crack but brittle cleavage can occur after the emission of a sufficient number of dislocations. The fracture process occurs as a combination of dislocation emission/micro-cleavage portions that are controlled by the local atomistic structure of the grain boundary. The grain boundary is shown to be a region where dislocation emission is easier, a mechanism that competes with the lower cohesive strength of the boundary region.

Some aspects of forces and fields in atomic models of crack tips

1991 ◽  
Vol 6 (12) ◽  
pp. 2565-2577 ◽  
Author(s):  
R.G. Hoagland ◽  
M.S. Daw ◽  
J.P. Hirth
Keyword(s):  
Crack Tip ◽  
Lattice Parameter ◽  
Crack Model ◽  
Dislocation Emission ◽  
Linear Elastic ◽  
Partial Dislocations ◽  
Atomistic Models ◽  
Crack Tips ◽  
Eam Potential ◽  
Crack Faces

This paper examines the stresses and displacement gradients in atomistic models of cracks based on an EAM potential devised for aluminum. Methods for computing these quantities are described. Results are presented for two models differing in terms of the orientations of the crack relative to the crystal, a [100] (010) orientation that behaves in a brittle fashion and a [111] (110) orientation that emits partial dislocations prior to extending. Both models display lattice trapping. The stresses in the brittle crack model are compared with the linear elastic prediction and found to be in remarkably good agreement to within distances of about one lattice parameter of the crack tip and at the free surface where contributions from sources other than strain energy (e.g., surface tension) influence the results. Similar results are observed for the ductile model until dislocation emission occurs. The largest stresses that develop just prior to crack extension or dislocation emission are used to estimate the ratio of theoretical tensile strength to shear strength in this material. Eshelby's conservation integrals, F and M, are also computed. F is found to be essentially contour independent and in agreement with the linear elastic prediction in both models until dislocation emission occurs, at which point a large screening contribution arises from the emitted partials. The contour size dependence of M reveals some interesting features of the crack tip including a slight wobble of the crack tip inside its potential well with changing applied K and the existence of forces acting to move the crack faces apart as blunting occurs.

Modeling of crack tip dislocation emission in B2 intermetallic alloys

1992 ◽  
Vol 7 (4) ◽  
pp. 919-925 ◽  
Author(s):  
Michael F. Bartholomeusz ◽  
John A. Wert
Keyword(s):  
Slip System ◽  
Fracture Mode ◽  
Crack Tip ◽  
Intermetallic Alloys ◽  
Dislocation Emission ◽  
Thermally Activated ◽  
Ordered Intermetallic ◽  
Macroscopic Fracture ◽  
Crack Tips ◽  
Active Slip

A model has been previously proposed to describe the energy associated with emission of dissociated superlattice dislocations from crack tips in ordered intermetallic alloys. In the present paper, the model is applied to several B2 intermetallic alloys. The results of the analysis reveal a correlation between the range of slip system orientations for which emission of a dislocation from a crack tip is energetically favorable and the macroscopic fracture mode of the alloy. Additionally, the effects of changing the active slip system, increasing the thermal energy available for thermally activated dislocation emission, and changing the {111} APB energy on the fracture mode of NiAl and FeAl are discussed.

A Combined Boundary Integral Method for Analysis of Crack Problems in Multilayered Elastic Media

2016 ◽  
Vol 08 (05) ◽  
pp. 1650070 ◽  
Author(s):  
Gongbo Long ◽  
Guanshui Xu
Keyword(s):  
Integral Method ◽  
Crack Tip ◽  
Boundary Integral ◽  
Thin Layers ◽  
Boundary Integral Method ◽  
Displacement Discontinuity ◽  
Elastic Media ◽  
Integral Methods ◽  
Crack Problems ◽  
Comparable Accuracy

An efficient and accurate elastic analysis based on boundary integral methods is presented for crack problems in inhomogeneous elastic media consisting of a set of individually uniform strata. The method combines the direct boundary integral method (DM) and the displacement discontinuity method (DDM) so that it shares both the efficiency of the DDM and the broad applicability of the DM. The DDM is implemented to construct the stiffness matrix in each layer, while the DM is used to characterize the effects of the interfaces. All the variables on the interfaces can then be eliminated through the continuity conditions, leading to the final system of equations consisting of variables on crack surfaces only. The concept of the crack tip element is also adopted for a better treatment of the crack tip singularity. The examples demonstrate that the combined method has comparable accuracy of DM but is more efficient, especially for the scaled thin layers in the application of practical hydraulic fracturing simulations.

scholarly journals Nonlinear two-dimensional free surface solutions of flow exiting a pipe and impacting a wedge

2021 ◽  
Vol 126 (1) ◽  
Author(s):  
Alex Doak ◽  
Jean-Marc Vanden-Broeck
Keyword(s):  
Surface Tension ◽  
Integral Equation ◽  
Free Surface ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Two Dimensional ◽  
Numerical Schemes ◽  
Additional Advantage ◽  
Infinite Wedge ◽  
Good Agreement

AbstractThis paper concerns the flow of fluid exiting a two-dimensional pipe and impacting an infinite wedge. Where the flow leaves the pipe there is a free surface between the fluid and a passive gas. The model is a generalisation of both plane bubbles and flow impacting a flat plate. In the absence of gravity and surface tension, an exact free streamline solution is derived. We also construct two numerical schemes to compute solutions with the inclusion of surface tension and gravity. The first method involves mapping the flow to the lower half-plane, where an integral equation concerning only boundary values is derived. This integral equation is solved numerically. The second method involves conformally mapping the flow domain onto a unit disc in the s-plane. The unknowns are then expressed as a power series in s. The series is truncated, and the coefficients are solved numerically. The boundary integral method has the additional advantage that it allows for solutions with waves in the far-field, as discussed later. Good agreement between the two numerical methods and the exact free streamline solution provides a check on the numerical schemes.

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