A New Formula for Evaluating Indentation Toughness in Ceramics

The Lawn-Evans-Marshall model for Vickers-induced crack driving force is widely applied for determining fracture toughness of ceramic materials, yet its simplification that the volumes of Vickers impression and equivalent expanding cavity merely depend on the half-diagonal length of residual impression will bring significant error. In this work, the model is modified by considering the influence of elastic recovery in depth after completely unloading on the volumes. As a result, a new expression for crack driving force is obtained and correspondingly a new fracture toughness formula is presented based on the modified model, which is expressed as the well-known Anstis formula with a different constant multiplied by the ratio of residual impression depth to the maximum indentation depth. Both finite element analysis and experimental results demonstrate the effectiveness of the proposed formula and, especially, that it works much better than Anstis formula on materials with large ratio of hardness to elastic modulus.