Hertzian cracks

The erosion of brittle materials has been described in terms of interacting Hertzian crack systems, or by the formation of lateral and median vents for sharp indentors. This is indicated in Figure 9.4. It has also been observed that brittle materials are capable of undergoing plastic deformation particularly when under erosion by very small particles.This is important because, at high temperature, some oxides formed as scales may show a ductile reaction to erosive impact. 

Hertzian crack suppression in ceramics with elastic-modulus-graded surfaces, Journal of the American Ceramic Society 81, 2301-2308. 

Fig. 8. (a) Schematic of a Vickers indentation-induced Hertzian cone crack, (b) View from the bottom of an aluminosihcate glass block of a Vickers... 

Figure 6.12. Hertzian cone crack evolution and geometry (Lawn 1993).

LGMs of the AT/alumina and AT/ZTA displayed some very interesting properties which include excellent machinability, low thermal expansion coefficient, improved thermal shock resistance, low hardness (about 5 GPa), low Young s modulus (E) (250 GPa) and excellent flaw tolerance [Pratapa, 1997 Pratapa Low, 1998 Skala, 2000 Manurung, 2001], These materials appeared to display a large degree of near-surface quasi-plasticity under the Hertzian or the Vickers indenter which effectively inhibits the formation and propagation of cracks. The ductile behaviour of these materials was... 

The fractures on a plane surface, created by the collisions of hard spherical particles at low-impact velocities, may form a conical crack according to the Hertzian quasi-static stress theory. In a multiple-impact situation, the conical cracks meet those extending from neighboring impact sites, and then the brittle material becomes detached. Once appreciable damage is done, the cracking mechanism may be altered because the particles no longer strike on a plane surface nevertheless the brittle removal continues by the successive formation and intersection of cracks. 

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). 

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 26. Typical cracks on the track of ball bearings (dry running under 1.75 GPa Hertzian pressure, 18 10 turns).

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...

For a water lubricated system we may however estimate the conditions quite differently. Considering that temperature rises because mechanical energy is transformed into thermal energy and assuming that water can be trapped in a confined space (between asperities, in superficial pores and/or cracks) the pressure would rise only due to the isochoric heating process. These pressures are in the order of several hundred Wa and thus still very high but much lower then those running into tens of GPa from Hertzian theory (Fig. I). 

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 iC-field as function of cone crack length and for increasing loads pf p// p/// (tuj-ing sphere-on-flat normal indentation of brittle materials. Arrowed seg-...

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