Experiments for Evlauating 3-D Effects on Cracks in Frozen Stress Models

Abstract

In the experimental work conducted, two cases have been considered for the six- finned internal star cylinder: the semi-elliptic natural crack and a machined V-cut crack extending the length of the cylinder, both originating from the axis of symmetry of the fin tip. The V-cut crack constitutes a plane strain approximation and is used in current design rationale. Results show that the normalized stress intensity factor (SIF) for the V-cut case are at least equal to, but in most cases are greater than, the natural crack cases. These results were compared to experimental results from Smith and his associates for motor grains having similar shaped off-axis cracks, and similar trends were achieved. Comparisons were also made between the natural crack models and the modified boundary element method of Guozhong, Kangda, and Dongdi (GKD) for a semi-elliptic crack in a circular cylinder and the V-cut crack models to the modified mapping collocation technique of Bowie and Freese (BF), which constitutes the plane strain solution to a circular cylinder with a crack extending the length of the bore. For both cases general trends were similar. Using the numerical results, a relation for estimating the plane strain SIF for the finned cylinder models was developed. The situation of a finned cylinder containing a crack the length of the bore constitutes the worst case scenario. Testing has shown, however, that under normal loading conditions this case is conservative. Penetration tests have shown that a crack penetrating the outer boundary retains its semi-elliptic shape, thus the use of a semi-elliptic crack in design more accurately represents reality.