Evaluation of the Fatigue Strength of Notched Geometries Using a Microstructural Model and Generative Algorithms

In this work, the assessment of a short crack emanating from arbitrarily shaped notches under Mode I loading is done. A parametric algorithmic tool is used to create a wide range of different two dimensional notch shapes for the evaluation of notch fatigue strength by means of the Distributed Dislocation Technique. Comparisons between V-notches, U-notches and semi-elliptical notches establishing similar geometrical parametric relations are shown, so that the simplicity and versatility of the designed tool is demonstrated. This useful properties and advantages make this tool applicable to industrial problems such as the modelling and assessment of the effect of corrosion pits on fatigue strength.

Anti-plane stress analysis of a half-plane with multiple cracks by distributed dislocation technique in nonlocal elasticity

The effective role of a distributed dislocation technique accompanied by a nonlocal elasticity model has been demonstrated for the crack problem in a half-plane. The dislocation solution is employed to model and analyze the anti-plane crack problem for nonlocal elasticity using the distributed dislocation technique. The solution of dislocation in the half-plane has been extracted through the solution of dislocation in an infinite plane by the image method. The dislocation solution has been utilized to formulate integral equations for dislocation density functions on the surface of a smooth crack embedded in the half-plane under anti-plane loads. The integral equations are of the Cauchy singular type, and have been solved numerically. Multiple cracks with different configurations have been solved; results demonstrate that the nonlocal theory predicts a certain stress value in the crack tip.

Application of Singular Integral Equation to a Crack Moving near a Hole in a Two-Dimensional Infinite Plate

In this study, crack path simulation was conducted based on a singular integral equation formulated by a continuous distributed dislocation technique. The problem investigated in this study was to predict the propagation path of a crack moving in an infinite elastic plate with a circular hole, under uniform tensile loading. In order to perform this prediction, a probing method was developed to search for a crack moving direction where the mode II stress intensity factor would be almost zero, enabling the crack to automatically extend in that direction. Some cases for different locations of an initial straight crack were simulated using the program developed.

Crack interaction with nanoscale twinning near a second-phase particle in fine-grained magnesium alloy

A theoretical model is established to address the effect of nanoscale twinning near a second-phase particle on crack growth in fine-grained magnesium alloys. The numerical solutions of singular integral equations are obtained by the considering complex variable method of Muskhelishvili, the superposition principle of elasticity, and the distributed dislocation technique. The expressions of stress intensity factors near the left crack tip are derived, and the energy release rate (ERR) characterizing the condition for crack propagation is also calculated. The influences of relevant parameters such as the location of nanoscale twin, the size of particle, and the relative distance between the inhomogeneity and the left crack tip on the ERR are examined in detail. The results indicate that the ERR is strongly influenced by the nanoscale twinning and the second-phase particle. The hard inhomogeneity decreases the ERR while the soft inhomogeneity increases the ERR when nanoscale twinning is not taken into account. At the same time, there is competition between the effects of the hard particle and nanoscale twinning on the ERR, and the nanoscale twin band with an optimum size displays the best toughening effect.