Elliptical Subsurface Cracks Under a Normal Stress and a Residual Stress Field

Abstract

Abstnx-Tbe distribution of residual stresses due to surface treatments, such as nitriding, induction hardening or shot-peening, is explained in the introduction. The stress intensity factor distribution along an elliptical plane crack near the surface in such a residual field is presented. Existing methods including the weight function method do not allow one to find this distribution directly. Therefore, a finite element study was undertaken showing the complex character of the stress intensity factor distribution. Additionally, the calculation of the stress intensity factor distribution around the crack front for an external tension or bending load stress is explained. In these cases some simplified semi-analytical expressions can be found.

Stress intensity factors for embedded cracks within torsionally loaded square prismatic bars

“…These graphical presentations of SIFs variations under shear mode for penny crack may serve as a complement, albeit brief, to the opening mode results developed by authors mentioned earlier. [18][19][20][21]…”

“…Of practical interest is the variation of SIFs for penny crack situated close to the free surface and corner as illustrated in Figure 17. Smith and Alavi, 18 Fischer et al, 19 and Shah and Kobayashi 20 presented some results for crack under opening mode near the free surface; Kobayashi et al 21 evaluated the tensile crack near a square corner. No results of any kind have been reported to date in the literature for penny cracks situated near free surface or corner loaded by shear stress.…”

“…An approximate variation of shear mode SIFs for a penny crack located near the free surface and the square corner is also reported. This brief graphical description represents the first report on shear mode penny crack situated near the free surface and the square corner, and may complement the work on opening mode by Smith and Alavi, 18 Fischer et al, 19 Shah and Kobayashi, 20 and Kobayashi et al 21 All simulation results are performed using the fracture mechanics package of Beasy, 30 a relatively new program based on the dual boundary element method (DBEM). Notwithstanding the need for vigorous assessment on a broader scale, especially in terms of accuracy, convergence, and flop count, its validity has been variously confirmed for problems described in the literature.…”

“…Of great practical interest is the study of crack situated near the free boundary. Smith and Alavi, 18 Fischer et al, 19 and Shah and Kobayashi 20 analytically treated the problem of a tensile crack close to the free surface of the half space; Kobayashi et al 21 presented a procedure for estimating the SIFs for tensile cracks near a square corner. No corresponding results for shear mode SIFs are available in the literature.…”