Gradient enriched linear-elastic crack tip stresses to estimate the static strength of cracked engineering ceramics

摘要

According to Gradient Mechanics (GM), stress fields have to be determined by directlyincorporating into the stress analysis a length scale which that takes into account the material microstructuralfeatures. This peculiar modus operandi results in stress fields in the vicinity of sharp cracks which are no longersingular, even though the assessed material is assumed to obey a linear-elastic constitutive law. Given both thegeometry of the cracked component being assessed and the value of the material length scale, the magnitude ofthe corresponding gradient enriched linear-elastic crack tip stress is then finite and it can be calculated by takingfull advantage of those computational methods specifically devised to numerically implement gradient elasticity.In the present investigation, it is first shown that GM’s length scale can directly be estimated from the materialultimate tensile strength and the plane strain fracture toughness through the critical distance value calculatedaccording to the Theory of Critical Distances. Next, by post-processing a large number of experimental resultstaken from the literature and generated by testing cracked ceramics, it is shown that gradient enriched linearelasticcrack tip stresses can successfully be used to model the transition from the short- to the long-crackregime under Mode I static loading.