Solution Of Crack Problems Research Articles

Slicing procedure for approximate three-dimensional Green's functions for cracks in plates of finite thickness

Exact results for the stress intensity factor are presented for an external circular crack with oppositely directed concentrated loads applied to the crack surfaces. This result is specialized to the case of a semi-infinite crack in an infinite body with concentrated loads on the crack. A procedure is then suggested by which one can obtain from the corresponding plane result the approximate three-dimensional Green's function (concentrated load result) for any straight crack in an infinite elastic body. This procedure is used to determine the Green's functions for a finite-length crack in an infinite body, and is then used in conjunction with a suggested “slicing” procedure to obtain approximate three-dimensional Green's function for plates of finite thickness and infinite extent, containing finite length cracks. Previously existing solutions for crack problems are compared with results obtained by application to plate tension and bending problems of the three-dimensional Green's functions. The results indicate that the procedure yields satisfactory results when stress gradients through the plate thickness are not excessive. However, an accurate assessment of the validity of the slicing procedure awaits further progress in three-dimensional crack analysis.

On the stresses in the vicinity of an elliptic hole in a cylindrical shell under torsional loading

A perturbation solution is presented for the stresses around a small elliptic hole in an infinitely long circular cylindrical shell subjected to torsion. The major axis of the whole is taken to be parallel to the shell axis. For the limiting case of a crack, the general solutions in elliptic coordinates are expanded at the crack tip in polar coordinates to obtain stresses in the form usual to solutions for crack problems.

The Treatment Of Crack Propagation InInhomogeneous Materials Using TheBoundary Element Method

The purpose of this paper consists in the implementation of a boundary element model for which the crack propagation is easily studied thanks to an automatic remeshing process. The traction singular quarter point element was used in order to improve the accuracy of the values of stress intensity factors. The Erdogan and Sih criterion allows us to determine the new growth direction after each step. Validity of this implement is demonstrated, with respect to experimental results, by the example of a holed plate. In this study, we can show the manner in which the crack may propagate when the distance between the initial crack's axis and the tangent hole is changed. Two distinct behaviours can be pointed out with respect to this distance : in some cases the crack may be simply deflected by the hole, and propagates across the plate until a complete fracture is reached. In other ones, the crack propagates toward and reaches the hole. In the framework of fatigue under cyclic loading, the manner in which growth rate is affected by the proximity of a hole is shown. INTRODUCTION The use of the Boundary Element Method for the solution of crack problems has been of interest to many investigators over recent years. However, for non-symetric problems where the two crack surfaces have the same geometrical coordinates, the direct application of this method leads to a singular system of equations. Some special techniques have been established to overcome this difficulty. The most general are the subregions method introduced by Blandford et al [1] and the dual bondary element method established by Portela et al [2]. In our study we have used the first method for the modelisation of the crack problems. We have shown [3] that the use of this method does not alter the automatization of crack propagation. Transactions on Engineering Sciences vol 6, © 1994 WIT Press, www.witpress.com, ISSN 1743-3533 376 Localized Damage THE BOUNDARY ELEMENT METHOD The boundary integral equation relates displacements i% and t< on the boundary F of an elastic homogeneous isotropic body. It can be written as : , Q)uj(Q)dT(Q) = f 0y (P, Q)ti(Q)dT(Q) (1) Jr In which the tensors T^ and Uij are the components number j of the tractions and displacements at Q due to a unit i direction load at P. The term Cij represents the behaviour of the singularity in Ty. When P is on a smoothpart of T, Cij = &,/2. Uj and tj denote components of the boundary displacement vector and the traction vector respectively. The boundary is now divided into N isoparametric elements. By using a collocation method, the system of equations is produced on the form : M {«}=[«]« (2) The matrices [A] and [J3] contain coefficients of either Tij and U . METHOD FOR THE CALCULATION OF STRESS INTENSITY FACTOR 'SIP' In order to evaluate correctly and accuratly the stress intensity factor, we have compared several methods like : the J Integral, Traction Singular Quarter Point Element (TSQP) and the Crack Opening Displacement method in which Kj is calculated for different formulations : Figure 1. Quarter point element /c = (3 — 4f/) for plane strain and =(3 — %/)/(! + %/) for plane stress In figure 2, we denote as follows : Quarter point elements and one-point displacement formula Quarter point elements and two point displacement formula Traction singular quarter-point elements and one-point displacement formula Traction singular quarter-point elements and two-point displacement formula Traction singular quarter-point elements and nodal value formula The extrapolation method of the displacement The crack size and the lenght of the element at crack tip KIUIS

Transform Solutions of Crack Problems in the Theory of Elasticity

Transform Solutions of Crack Problems in the Theory of Elasticity