Continuum versus discontinuum damage mechanics of creep caused by microcracking

摘要

The effect of evolution of damage, mainlymicrocrack damage, on creep and creep fracture of brittlematerials (or materials exhibiting brittle-like behavior undercertain temperature and loading conditions) is treatedtheoretically. A comparative analysis of two basic approaches is given:(I) continuum damage mechanics (CDM), and(II) discontinuum damage mechanics (DDM). The firstapproach deals, from the very beginning, with continuumabstract description of damage with the help of field quantities.The second approach considers the macroscopic mechanicalbehavior of the material affected by damage evolution in termsof individual damage units, such as microcracks or/andmicrovoids. A serious conceptual deficiency of the CDMapproach is pointed out and analyzed. This deficiency isassociated with the CDM basic notion of the effective stress,understood as the stress (referred to undamaged area) whichgoverns the deformation of the material per se in the presence ofdamage. This deficiency becomes apparent in the case whendamage is caused a multitude of cracks (microcracks). In thiscase, the damaged area, as it is defined by CDM, is actually thearea occupied by cracks. As this area is negligible, the effect ofdamage on the mechanical behavior of the material, according toCDM, would be negligible either, irrespective of the cracksconcentration, which is in contradiction with reality. It is shownhow the situation can be improved with the aid of DDM andhow the macroscopic creep behavior relates to the structure andstrength parameters of the material when considering themechanism of damage evolution in terms of thermal activation.