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. Closed-form 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 fracture, grinding and polishing and common cutting and machining operations.