Stress Intensity Factor Estimates for a Peripherally Cracked Spherical Void and a Hemispherical Surface Pit

Abstract

Stress intensity factors are estimated for three‐dimensional defects which occur in ceramic bodies. The two idealized cases considered are a spherical void with a circumferential crack at its equator stressed by uniaxial tension at infinity and a hemispherical pit at a free surface of a semi‐infinite body also stressed by uniaxial tension with a circumferential crack at the semiequator of the pit. These stress intensity factors, which are given as a function of the crack length L to radius R of the spherical void or hemispherical pit, are considered as estimates because of the approximate nature of the analysis.

Effect of Grain Size on Mechanical Properties of Submicrometer 3Y‐TZP: Fracture Strength and Hydrothermal Degradation

“…In this case, the dependence of fracture strength on grain size is small but is more dependent on the geometry of the fracture origin. The use of a model geometry for alumina shows good agreement between theory and experiment for a spherical pore with an adjacent semicircular crack 7,8 …”

“…The use of a model geometry for alumina shows good agreement between theory and experiment for a spherical pore with an adjacent semicircular crack. 7,8 The critical stress for microcrack formation decreases with increasing grain size as has been demonstrated by Hoffman and colleagues 3,4 on alumina using acoustic emission (AE). Below a critical grain size, model calculations suggest that failure is caused by the stress concentrations around the pore before a microcrack can form.…”

Stress intensity factors and weight function for a void with an annular crack

“…Several estimative stress intensity factor solutions of this crack problem are proposed in the literature [1][2][3][4]. An extended intercomparison of the results is given in [5].…”

“…5. The annular crack loaded by a constant stress yields the geometric function 1.1222 [ 1 ]~/o~+2 F-(l+2¢x)2+ 1 (l+~cx)2 o~+1 (15) and is plotted in Fig. 6 together with the penny-shaped crack approximation [3].…”

“…Stress intensit factor for cracks around spherical pores;short-dashed line[1][2], dasl dotted line[3], long-dashed line[4] ; solid lines: upper and lower boundaries (~=0.Interpolation of limit cases.Solid line: stress intensity factors interpolated according to(9); circles: results from[7] (Body Force Method), other lines as described inFig. 2.Int Journ of Fracture 67 (1994) Comparison of two solutions for remote tension loading.…”