Cohesive interface simulations of indentation cracking as a fracture toughness measurement method for brittle materials

Cracks in brittle solids induced by pyramidal indenters are ideal for toughness evaluation since the indentation stress fields decay rapidly from the contact center and any cracks will be eventually arrested. Thus, if the applied energy release rate can be determined analytically, the material toughness can be deduced by measuring the crack length. However, such a driving force calculation is a nontrivial task because of the complex stress fields; only a number of limit cases can be solved, such as the long half-penny cracks (at least two times larger than the contact size) in the classic Lawn-Evans-Marshall (LEM) model. Important questions such as the evolution from short cracks to median/radial and then to half-penny cracks, the form of the scaling relationship that relates fracture toughness to material hardness and indenter angles, the threshold load for indentation cracking, etc., cannot easily be answered without a detailed knowledge of the co-evolution history of the stress fields and crack morphology. To this end, a finite element model of four-sided pyramidal indentation adopting cohesive interface elements is developed to study the effects of indenter geometry, load, cohesive interface parameters, and material properties on the initiation and propagation of the median/radial/half-penny crack systems. The validity and artifacts of the cohesive interface model are carefully examined, and the crack morphologies under various indentation and material parameters are systematically studied. Numerical predictions lead to a quantitative evaluation of the threshold load for indentation fracture, and an improved method for the evaluation of material toughness from the indentation load, crack size, hardness, elastic constants, and indenter geometry, which compare favorably to a large set of experiments in the literature. It is also found that the toughness evaluation method is very sensitive to Poisson's ratio - an observation that has previously received little attentions. An approximate analysis for short cracks is developed based on the fracture mechanics of annular cracks and the embedded-center-of-dilatation model for indentation-induced residual stress fields.