Crack Opening Profiles Research Articles

Stress intensity factors for cracked holes and rings loaded with polynomial crack face pressure distributions

The purpose of this report is to present some recent stress intensity factor solutions for cracked rings and holes which may be of general interest to other investigators. The present results are based on mode I solutions reported previously for radially cracked holes in large plates [I] and for radially cracked rings [2] loaded with an arbitrary crack face pressure. These through-thickness flaw geometries, showing the crack face pressure p(x), are presented in Fig. i. In addition to the single crack configurations shown, symmetric double flaws are also considered. Note that the ring geometry is limited to an aspect ratio Ri/R o = 0.5. As described in [I] and [2], stress intensity factor solutions for these two problems were obtained by weight function techniques and are given by K I = (H/K*) p(x) ~n/~a dx (1) o Here H is a constant which is defined by the modulus of elasticity and Poisson's ratio, K* is the known stress intensity factor for a given loading applied to the flaw geometry of interest, a is the crack length, x is the distance from the edge of the hole or bore of the ring, and is the crack opening profile corresponding to the known stress intensity factor solution K*. The solution for uniaxial tension described by Bowie [3] and reported in [4] was used for K* for the cracked hole problems, while the result obtained by Jones [5] for a point compressive load along the crack plane served as K* for the ring geometry. A convenient numerical technique for approximating the crack surface profile n and for computing the partial derivative ~n/~a is described in [I]. If the crack face pressure p(x) is defined as the unflawed hoop stress distribution next to the hole or ring when subjected to the loading of interest, (I) yields K I for the corresponding crack problem. This procedure was shown in [i] and [2] to give stress intensity factors which agree well with independent solutions for a variety of problems, as was recently used to obtain stress intensity factors for coldworked holes in aluminum plates and for autofrettaged cylinders [6]. The coldworking and autofrettaging processes involve introduction of residual stresses into the component by a radial expansion into the plastic range. The coldworked hole results agree well with corresponding experimental measurements and enabled accurate prediction of specimen fatigue lives, while the autofrettaged cylinder calculations agree favorably with previous solutions in the literature [7]. Thus, it is felt that these crack face pressure solutions are of practical use for analyzing fastener holes and thickwalled cylinders.

Stress field around a high speed screw dislocation : Shunya Ishioka, Materials Sciences Program, Brown University Providence, Rhode Island 02912, U.S.A.

Cracking phenomena in tensile-strained InxGa1−xAs epitaxial film on an InP substrate are analyzed via the formulation given in Part I [Lee, S., Choi, S.T., Earmme, Y.Y., 2006. Analysis of vertical cracking phenomena in tensile-strained epitaxial film on a substrate: Part I. Mathematical formulation. International Journal of Solids and Structures 43, 3401–3413], where the solution for a dislocation in an anisotropic trimaterial is used as a fundamental solution and the crack is modeled by the continuous distribution of dislocations. Misfit strains and stresses are evaluated as a function of indium content x in an InxGa1−xAs/InP system. A single crack and periodic cracks, respectively, induced by the misfit stresses are considered. The crack opening profile, the crack mouth displacement, and the energy release rate as a function of the crack length are obtained. The critical conditions for a single crack and periodic cracks, respectively, are thus obtained, and are found to depend on the film thickness, the crack length, and the period of the cracks. The results of these analyses are also compared with published data obtained from experiments.

A comparison of finite-element and experimental studies on the deformation of zirconium notched bend specimens

In earlier work, A.R. Luxmoore and P.J. Wyatt described measurements of the deformation of zirconium notched bend specimens, using the Moiré effect. This deformation has been simulated by a two-dimensional elastic-plastic finite-element program, and small variations of the crack geometry studied. The numerical and experimental results were compared by studying (a) the crack opening displacement, (b) the crack opening profile, and (c) the size and shape of the plastic zones.