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

Abstract

According to Gradient Mechanics (GM), stress fields have to be determined by directly incorporating into the stress analysis a length scale which that takes into account the material microstructural features. This peculiar modus operandi results in stress fields in the vicinity of sharp cracks which are no longer singular, even though the assessed material is assumed to obey a linear-elastic constitutive law. Given both the geometry of the cracked component being assessed and the value of the material length scale, the magnitude of
the corresponding gradient enriched linear-elastic crack tip stress is then finite and it can be calculated by taking
full 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 material
ultimate tensile strength and the plane strain fracture toughness through the critical distance value calculated
according to the Theory of Critical Distances. Next, by post-processing a large number of experimental results
taken from the literature and generated by testing cracked ceramics, it is shown that gradient enriched linearelastic crack tip stresses can successfully be used to model the transition from the short- to the long-crack
regime under Mode I static loading.