On the mechanics of surface and side-wall chipping from line-wedge indentation

Abstract

Chipping in glass plates from line-wedge contact loading is studied as function of the wedge's subtended angle 2β, its inclination angle φ, and the distance h from a corner having a subtended angle 90 • −θ . A brittle-fracture analysis in conjunction with the FEM technique is used to elucidate the role of geometric variables on chip morphology and chipping load. Closedform relations are developed for the latter by invoking the principle of geometric similarity and taking into consideration the details of contact forces transmitted to the crack mouth. The fracture progresses stably until surface effects alter the crack trajectory to form a chip. The latter conclusively occurs from the top surface if φ > β while from the side wall if φ < β. The fracture load for top-surface spalling scales with w 1/2 , where w is the indentation depth, and it monotonically declines with the offset angle ψ ≡ φ − β, that for side-wall chipping scales with h 1/2 and it is little sensitive to φ for moderate values of θ . In both the cases, the chipping load increases with β. The results may provide insight into the mechanics of chipping in more complex anthropological, tribological, geological and biomedical applications, including flint-knapping, dental Herzl Chai-On leave, School of Mechanical Engineering, fracture, grinding and polishing and common cutting and machining operations.

On the chipping and splitting of teeth

“…The potential also exists, at the lower end of h, for chips to emerge on the same top surface as that of the contact rather than on the side wall. Such an occurrence is especially favored by ultra-sharp indenters loaded tangentially to the tooth surface (Chai and Ravichandran, 2007). This kind of limited microfracture event may be considered to be more in the realm of wear than of full-scale failure.…”

“…Attention has focused on the fracture force P F required to produce a chip of characteristic dimensions C and D in a solid with a well-defined edge geometry. A recent analysis has provided simple explicit equations relating these quantities to the distance h of the contact point from the free edge and (in the case of P F ) to the material toughness K C (Chai and Lawn, 2007b;Chai and Ravichandran, 2007). Tests on model brittle solids such as glass and fine-grain ceramics have validated these equations.…”

On the mechanics of edge chipping from spherical indentation

“…Other factors affecting the chipping load and chip morphology are indenter stiffness (Pelcin 1997a), orientation of indenter axis relative to indented surface (Speth 1975;Chai and Lawn 2007b), orientation of side wall relative to indented surface (Pelcin 1997b; Danzer et al 1997;Chai and Lawn 2007b;Mohajerani and Spelt 2010;Chai et al 2010), tangential loading component (Petit et al 2009) and material anisotropy (Zaayman et al 2009). As shown in Chai and Ravichandran (2007), acute indenters propelled nearly tangentially to a surface may cause chipping on the indented (top) rather than side surface, a configuration relevant to wear. For oblique spherical indentation on non-orthogonal surfaces, chipping may occur by the extension of a cone crack (Cotterell and Kamminga 1987), as opposed to median cracks in the present surface-normal loading.…”

“…Our analysis is limited to low-velocity spherical impact; the case of Vickers impact has been considered elsewhere (Chai and Ravichandran 2007). The maximum load transmitted to the target in this case is generally evaluated assuming quasi-static load transfer in conjunction with Hertz's elastic contact analysis (Timoshenko and Goodier 1970).…”

“…The maximum load transmitted to the target in this case is generally evaluated assuming quasi-static load transfer in conjunction with Hertz's elastic contact analysis (Timoshenko and Goodier 1970). Using this approach, Chai and Ravichandran (2007) obtained the following expression for the threshold impact energy needed to cause chipping…”