Hertzian ring crack

I. Finnic and S. Vaidyanathan, Initiation and propagation of hertzian ring cracks. In Fracture Mechanics of Ceramics, eds., R. C. Bradt, D. P. FI. Hasselman, and F. F. Lange, New York, Plenum Press, 1974, p. 231. 

Figure 12.5 Contact damage (cracks) in the surface of ceramics, (a, b) Cracks caused by a blunt and (c, d) cracks caused by a sharp indenter. (a) Hertzian ring crack in silicon carbide (b) Crack caused in operation by the...

Figure 5.18. Relationship between probability of Hertzian ring crack formation and load for difierent-sized steel indenters on flat surface of a brittle ceramic.

Fig. 17 Contact mechanics analysis of Herztian cracks within brittle materials.a Schematic description of a Hertzian cone crack induced under normal indentation by a rigid sphere, b Reduced plot of JC-field as function of cone crack length and for increasing loads pf < p// < pm during sphere-on-flat normal indentation of brittle materials. Arrowed segments denote stage of stable ring crack extension from Cf to cc (initiation), then unstable to ci at P = P,n (cone-crack pop-in) (From [67]). Branches (1) and (3) correspond to unstable crack propagation (dK/dc > 0), branches (2) and (4) to stable crack propagation (dK/dc < 0)...

All fracture surfaces were analysed by ffactographic means in order to identify fracture origins. In any case the fracture origins are at or very close to the surface. In the case of set C, the surface flaws identified by the dye penetrant and positioned in the highest loaded area of the specimens were fracture origins in every case. An example is shown in Fig. 6.b. The fracture origin is a Hertzian contact crack (a part of a ring crack), which had previously been detected before fracture (Fig. 6.a). 

As the contact circle passes over the ball surface, the crack front will pass from compressive to tensile stress continuously. When the crack lies in the compressive region (-2a < x < 0), the crack is suppressed (K < 0). Consequently, the crack front will not propagate along the main growth path in the compressive region. However, subsequent surface cracks may occur due to the pre-existence of ring cracks, and the branch cracks on the crack faces may also occur due to the crack face contact. The co-ordinate x affects the subsurface behaviour, which may be a rather complex process due to Hertzian loading in a cyclic fashion. 

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