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Based on the asymptotic stress fields including higher order terms at the crack tip of a non-linear material, conditions under which single or double parameter controlled onset of fracture initiation occur are discussed. A set of experimental data under cleavage fracture was analysed. It is shown that under Mode I plane strain conditions two parameters J and A₂ can be utilized to predict the onset of fracture with J setting the loading level and A₂ relating to the constraint. Theoretical meanings of fracture toughness values corresponding to conditions of small scale yielding and the HRR stress distribution are discussed. A procedure of applying this concept to the evaluation of flawed structures is outlined.