A novel multiscale approach to brittle fracture of nano/micro‐sized components

Abstract

Principles and advantages of a new concept based on the ab initio aided strain gradient elasticity theory are shown in comparison with the classical Barenblatt cohesive model. The method is applied to the theoretical prediction of the critical energy release rate and the crack tip opening displacement at the crack instability in nanopanels made of germanium and molybdenum crystals. The necessary length scale parameter l1 is determined for germanium and molybdenum by the best gradient elasticity fits of ab initio computed screw dislocation displacements and phonon dispersions. Values of ab initio computed critical energy release rates and crack opening profiles revealed that the length l1 is related to inflexion points of profiles. A novel ab initio method in combination with continuum mechanics was successfully tested to replace molecular statics dependent of availability of interatomic potentials. The asymptotic strain gradient elasticity solution for displacement components near the crack tip in materials with cubic lattice was also derived.

Higher-order asymptotic crack-tip fields in simplified strain gradient elasticity

“…We can also mention Refs. [68,69], where the similar numerical solutions for the crack problems have been obtained.…”

“…These results are typical for SGE and similar solutions have been obtained previously for the crack problems in Refs. [8,68,69]. In this full-field solution, the normal strains have maximum (but finite) concentration at the crack tip (Fig.…”

“…Such example for n = 6 is given in (69). For the sub-series numbers n = 4s, s ∈ N we can use a n , d n+4 to provide t…”

Nonlocal analysis of edge‐cracked nanobeams under Mode I and Mixed‐Mode (I + II) static loading

“…In the context of cracked nanostructures under static loading, that is, the loading condition examined in the present research work, both atomistic modeling [19][20][21][22][23][24][25][26][27][28] and GCTs [29][30][31][32][33][34][35][36][37][38][39] are put forward into several studies to investigate their fracture behavior, being the experimental investigation still a challenge, due to technical difficulties connected with the nanoscale sizes involved.…”

Temperature Dependence of Fracture Characteristics of Variously Heat-Treated Grades of Ultra-High-Strength Steel: Experimental and Modelling

“…Recently, the strain-gradient fracture mechanics coupled with atomistic approaches was utilized to eliminate the stress singularity at the crack tip and to predict FT for components sized in the entire range from macro to nano (e.g., [ 9 ]). This method is numerically complex and time consuming and, up to now, its verification was done only for single crystals of several pure metals and ceramics [ 10 ].…”