The ab-initio aided strain gradient elasticity theory: a new concept for fracture nanomechanics

Abstract

When the width of cracked nanocomponents made of brittle or quasi-brittle materials is less than approximately , the size of the - dominance zone becomes smaller than  and comparable to the fracture process zone ( ). The fracture process starts to be dominated by far-stress field terms and the critical stress intensity factor can no more represent the total fracture driving force. This means a breakdown of a classical linear elastic fracture mechanics suffering from the undesirable crack-tip stress singularity. The contribution presents a new concept expected to properly predict the critical crack driving force for nano-components: The ab-initio aided strain gradient elasticity theory (AI-SGET). In contrast to the Barenblatt cohesive model, the strain gradient elasticity theory does not require to prescribe a suitable field of cohesive tractions along the crack faces in order to eliminate the stress singularity and to exhibit cusp-like profiles of crack flanks close to the crack front in accordance with atomistic models. The only unknown and necessary quantity is the material length scale parameter which can be, e.g., determined by best strain gradient elasticity fits of ab-initio computed phonon-dispersions and near-dislocation displacement fields. Atomistic approaches can also be employed to determine fracture mechanical parameters (crack driving force, crack tip opening displacement) related to the moment of crack instability in a given material.  Such AI-SGET codes can then be utilized to a successful prediction of fracture of cracked nanocomponents made of brittle or quasi-brittle materials.