Modelling of grain size effects in creep crack growth using a non-local continuum damage approach

The local creep continuum damage finite element method is incapable of modelling the size effect observed in experiments between large and small cracked tension specimens. A new finite-domain non-local damage method is developed to overcome this difficulty. The concept of a material characteristic dimension is introduced in which cellular regions of the finite element mesh are defined to damage at the same rate. The size of the cellular regions is related to the characteristic dimension and to how continuum damage evolves on the microscale. This new method is shown to predict the experimentally determined differences in the damage distributions, and in the failure times between geometrically similar large and small cracked tension specimens. A non-local damage technique using infinite domain cellular regions is shown to be incapable of predicting the size effect. The ability of the finite domain non-local damage method to predict the size effect is due to the relationship between discrete cellular regions of the finite element model and the physical characteristics of the material modelled, by spatially averaging the local damage rate parameter over a material characteristic volume.