Engineering topics
Publications and source records attributed to Hartranft, R. J..
A combination of longitudinal shear and normal forces acting on a half-plane crack is shown to lead to predictions of crack growth qualitatively similar to those obtained by Knauss (1970) for crack propagation in antiplane shear. The presented results, based on the strain-energy-density fracture criterion, predict the direction of growth and the load which initiates it.
Methods for solving three dimensional crack problems are discussed. The stress intensity factor for the case of uniform pressure on the surface crack is analysis. An analysis of concentrated forces acting on the crack faces parallel to the crack front of a half-plane crack was made. Two dimensional calculations were made using the exact solution for the stress field around an elliptical hole in a uniformly stretched plate. The strain energy density was computed in the neighborhood of the ends of narrow, but sharp, ellipses.
The closed form expressions for the stress intensity factors due to concentrated forces applied to the surfaces of a half plane crack in an infinite body are used to generate solutions for distributed loads in this geometry. The stress intensity factors for uniformly distributed loads applied over a rectangular portion of the crack surface are given in closed form. An example of non-uniformly distributed loads which can be treated numerically is also included. In particular, combinations of normal and shear stresses on the crack which simulate the case of loading at an angle to the crack front are considered. The resulting stress intensity factors are combined with the strain energy density fracture criterion for the purpose of predicting the most likely direction of crack propagation. The critical value of the energy density factor can then be used for determining the allowable load on a specimen with a crack front not perpendicular to the tensile axis.
An analytical model of a through-thickness crack in a statically stretched plate is presented in which the crack front stress state is permitted to vary in the direction of the plate thickness. The amplitude or intensity of this stress field can be made nearly constant over a major portion of the interior crack front which is in a state of plane strain. The average amount of work available for extending a small segment of the crack across the thickness is associated with an energy release rate quantity in a manner similar to the two-dimensional Griffith crack model. The theoretically calculated energy release rate is shown to increase with increasing plate thickness, indicating that available work for crack extension is higher in a thicker plate.
The alternating method, which intimately combines analytical results with numerical calculations, as applied to edge crack problems in two dimensions and surface crack problems in three dimensions, is treated. The case of a crack perpendicular to the edge of a semiinfinite material is considered. One of the crack geometries that has received continual interest in fracture mechanics is that of a semielliptical crack whose major axis lies on a stress free surface. In order to demonstrate the sensitivity of the solution to the influence of the free surface the semicircular crack problem is again treated by the alternating method.
The Schwarz-Neumann alternating method is employed to obtain stress intensity solutions to two crack problems of practical importance: a semi-infinite elastic plate containing an edge crack which is subjected to concentrated normal and tangential forces, and an elastic half space containing a semicircular surface crack which is subjected to uniform opening pressure. The solution to the semicircular surface crack is seen to be a significant improvement over existing approximate solutions. Application of the alternating method to other crack problems of current interest is briefly discussed.
Elastic plate uniform extension with rectangular crack by three dimensional bending theory, using variational principle
Eigenfunction expansion technique to analyze three dimensional crack and wedge problems, emphasizing stress field near straight edged crack
Approximative three dimensional solution for crack in elastic plates
Plate thickness effect on bending stress near crack front for plates with through cracks
Eigenfunction expansion technique for three dimensional stress and displacement expressions in series form for infinite solids weakened by plane of discontinuity or crack
Theoretical study of plate thickness effect on bending stress distribution around slotted cracks