Sub-critical crack extension and crack resistance in polycrystalline alumina

Sub-critical crack extension can readily be observed in controlled fracture tests in fourpoint bending. A natural crack of any desired lengthc which exceeds the notch depthc ₀ by the amount c =c –c ₀ can be introduced into bend specimens by stable crack propagation. The stress intensity factor to achieve c increases considerably with increasing c. In pre-cracked specimens the stress intensity factorK _I0 to start the crack and the critical valueK _IC strongly depend on the natural crack length c whereasK _I0 andK _IC are independent ofc ₀ in solely notched specimens. From a quasi-continuous evaluation of the load-deflection curve recorded during controlled fracture, the differential work of fracture can be obtained as a function of the achieved crack length. It may be regarded as the crack extension resistanceR of the material because the balance between the energy release rateg ₁ andR is maintained throughout the experiment. By that, a formal analogy to theR-curve concept of fracture mechanics is given. The steady increase ofR is explained by multiple crack formation and by the interference of the fracture surfaces due to the angular development of the crack front.