Abstract
The contact mechanics of sharp “glass‐cutting” rollers is analyzed. Assuming the contact to be plastic, expressions are developed for the width and length of a static contact and the width of a rolling track. The residual stress‐intensity factor and stable length for median cracks generated beneath a roller track are derived, assuming the track to have been created by an equivalent wedge loading and modeling the plastic deformation zone as an expanding cylindrical cavity. The strengths of components containing dominant roller flaws are then derived by superposing an applied stress field onto the residual contact field and solving for instability. The contact dimensions, median crack lengths, and strengths are all expressed in terms of the roller radius and included angle, contact load, and indented material hardness, modulus, and toughness. Tests on soda–lime glass and aluminum confirm the predicted dependences.
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