Creep deformation at crack tips in elastic-viscoplastic solids

The evaluation of crack growth tests under creep conditions must be based on the stress analysis of a cracked body taking into account elastic, plastic and creep deformation. In addition to the well-known analysis of a cracked body creeping in secondary (steady-state) creep, the stress field at the tip of a stationary crack is calculated for primary (strain-hardening) or tertiary (strain-softening) creep of the whole specimen. For the special hardening creep-law considered, a path-independent integral C¹_h, can be defined which correlates the near-tip field to the applied load.It is also shown how, after sudden load application, creep strains develop in the initially elastic or, for a higher load level, plastic body. Characteristic times are derived to distinguish between short times when the creep-zones, in which creep strains are concentrated, are still small, and long times when the whole specimen creeps extensively in primary and finally in secondary and tertiary creep. Comparing the creep-zone sizes with the specimen dimensions or comparing the characteristic times with the test duration, one can decide which deformation mechanism prevails in the bulk of the specimen and which load parameter enters into the near-tip stress field and determines crack growth behavior. The governing load parameter is the stress intensity factor K₁ if the bulk of the specimen is predominantly elastic and it is the J-integral in a fully-plastic situation when large creep strains are still confined to a small zone. The C¹_h-integral applies if the bulk of the specimen deforms in primary or tertiary creep, and C¹ is the relevant load parameter for predominantly secondary creep of the whole specimen.