Stress Analysis of Contact Deformation in Quasi‐Plastic Ceramics

A stress analysis is made of Hertzian contact deformation in relatively tough ceramics with heterogeneous microstructures, where the response is essentially quasi‐plastic rather than ideally elastic‐brittle. Contact data for two such heterogeneous ceramics, a micaceous glass‐ceramic with modest hardness and a silicon nitride with high hardness, are presented as illustrative cases. Data from a soft steel serve as a comparative baseline. Two distinctive aspects of the deformation response are explored: indentation stress‐strain nonlinearity; and size and shape of the damage zone. For the harder ceramics, the stress‐strain nonlinearity is less pronounced, and the quasi‐plastic zone is more tightly confined beneath the contact, than in traditional ductile metals. As in metals, the deformation process in the ceramic structures is essentially shear driven, but has its origin in microstructurally localized interfacial sliding faults rather than in dislocation slip. Finite element modeling (FEM) is used to compute the shear stress distributions beneath the spherical indenters for selected experimental loading conditions. The underlying basis of the FEM calculations is an elastic‐plastic constitutive relation based on a critical shear condition for yield, but incorporating a strain‐hardening characteristic to allow for local elastic constraints on the sliding shear faults. The FEM calculations are able to simulate the main features of the stress‐strain curves and the evolving deformation zone geometries. In addition, the calculated tensile stress distributions are able to account, at least in part, for the suppression of conventional brittle fracture tendencies in tougher ceramics.